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MATHEMATICS (642 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 5)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 6)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)
Foundations and Trends® in Networking     Full-text available via subscription   (Followers: 1)

        1 2 3 4 | Last

Journal Cover Computational Methods and Function Theory
  [SJR: 0.329]   [H-I: 5]   [0 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1617-9447 - ISSN (Online) 2195-3724
   Published by Springer-Verlag Homepage  [2340 journals]
  • Approximation of functions by complex genuine Pólya-Durrmeyer
    • Authors: Vijay Gupta; Neha Malik
      Pages: 3 - 17
      Abstract: Abstract In this paper, the exact order of approximation and Voronovskaja type theorems with quantitative estimate for complex genuine Pólya-Durrmeyer polynomials attached to analytic functions on compact disks are obtained. Our results show that extension of the complex genuine Pólya-Durrmeyer polynomials from real intervals to compact disks in the complex plane extends approximation properties (with quantitative estimates).
      PubDate: 2017-03-01
      DOI: 10.1007/s40315-016-0167-x
      Issue No: Vol. 17, No. 1 (2017)
  • On the Characterisations of a New Class of Strong Uniqueness Polynomials
           Generating Unique Range Sets
    • Authors: Abhijit Banerjee; Sanjay Mallick
      Pages: 19 - 45
      Abstract: Abstract The purpose of the paper is to introduce a new class of strong uniqueness polynomials with the best possible answer to the question posed by the first author (Banerjee, Ann Acad Sci Fenn Math 40:465-474, 2015). We find the corresponding unique range set which improves a result due to Frank–Reinders (Complex Var Theory Appl 37(1):185–193, 1998). At the time of characterising the strong uniqueness polynomial, we also encounter the cases where the polynomial is not necessarily critically injective and find its degree and the corresponding unique range set. Furthermore, we find some connections between this new class of polynomials and most of the polynomials generating URSM introduced so far in the literature of value distribution theory. As an application of our results, we will show that the theorems improve many previous results. Lastly, we rectify the gap in the last section of An (Acta Math Vietnam 27(3), 251–256, 2002, p. 255, l. 11–14) and thus improve the result obtained by An (Acta Math Vietnam 27(3), 251–256, 2002) significantly.
      PubDate: 2017-03-01
      DOI: 10.1007/s40315-016-0174-y
      Issue No: Vol. 17, No. 1 (2017)
  • On Lappan’s Five-Point Theorem
    • Authors: Tran Van Tan; Nguyen Van Thin
      Pages: 47 - 63
      Abstract: Abstract A well-known result of Lappan states that a meromorphic function f in the unit disc \(\mathbb {D}\) is normal if and only if there is a subset \(E\subset \widehat{\mathbb {C}}\) consisting of five points such that \(\sup \{(1- z ^2) f^{\#}(z): z \in f^{-1}(E)\} < \infty ,\) where \(f^{\#}(z)\) is the spherical derivative of f at z. An analogous result for normal families is due to Hinkkanen and Lappan: a family \(\mathcal F\) of meromorphic functions in a domain \(D\subset \mathbb {C}\) is normal if and only if for each compact subset \(K\subset D,\) there are a subset \(E\subset \widehat{\mathbb {C}}\) consisting of five points and a positive constant M such that \(\sup \{f^{\#}(z): f\in \mathcal F, z \in f^{-1}(E)\}<M.\) In this paper, we extend the above-mentioned results to the case where the set E contains fewer points. In particular, the Pang–Zalcman’s theorem on normality of a family \(\mathcal F\) of holomorphic functions f in a domain D,  \(f^nf^{(k)}(z)\ne a\) (for some given constant a), is also extended to the case where the spherical derivative of \(f^nf^{(k)}\) is bounded on the zero set of \(f^nf^{(k)}-a\) .
      PubDate: 2017-03-01
      DOI: 10.1007/s40315-016-0168-9
      Issue No: Vol. 17, No. 1 (2017)
  • Escaping Endpoints Explode
    • Authors: Nada Alhabib; Lasse Rempe-Gillen
      Pages: 65 - 100
      Abstract: Abstract In 1988, Mayer proved the remarkable fact that \(\infty \) is an explosion point for the set \(E(f_a)\) of endpoints of the Julia set of \(f_a:\mathbb {C}\rightarrow \mathbb {C}; \mathrm{e}^z+a\) with \(a<-1\) ; that is, the set \(E(f_a)\) is totally separated (in particular, it does not have any non-trivial connected subsets), but \(E(f_a)\cup \{\infty \}\) is connected. Answering a question of Schleicher, we extend this result to the set \(\tilde{E}(f_a)\) of escaping endpoints in the sense of Schleicher and Zimmer, for any parameter \(a\in \mathbb {C}\) for which the singular value a belongs to an attracting or parabolic basin, has a finite orbit, or escapes to infinity under iteration (as well as many other classes of parameters). Furthermore, we extend one direction of the theorem to much greater generality, by proving that the set \(\tilde{E}(f)\cup \{\infty \}\) is connected for any transcendental entire function f of finite order with bounded singular set. We also discuss corresponding results for all endpoints in the case of exponential maps; to do so, we establish a version of Thurston’s no wandering triangles theorem for exponential maps.
      PubDate: 2017-03-01
      DOI: 10.1007/s40315-016-0169-8
      Issue No: Vol. 17, No. 1 (2017)
  • On the $$\varphi $$ φ -Hyperderivative of the $$\psi $$ ψ -Cauchy-Type
           Integral in Clifford Analysis
    • Authors: Ricardo Abreu Blaya; Juan Bory Reyes; Alí Guzmán Adán; Uwe Kähler
      Pages: 101 - 119
      Abstract: Abstract The aim of this paper is to introduce, in the framework of Clifford analysis, the notions of \(\varphi \) -hyperdifferentiability and \(\varphi \) -hyperderivability for \(\psi \) -hyperholomorphic functions where ( \(\varphi ,\psi \) ) are two arbitrary orthogonal bases (called structural sets) of a Euclidean space. In this study we will also show how to exchange the integral sign and the \(\varphi \) -hyperderivative of the \(\psi \) -Cliffordian Cauchy-type integral. Thereby, we generalize, in a natural way, the corresponding quaternionic antecedent as well as the standard Clifford predecessor.
      PubDate: 2017-03-01
      DOI: 10.1007/s40315-016-0172-0
      Issue No: Vol. 17, No. 1 (2017)
  • On the Relation Between Strebel Points and Infinitesimal Strebel Points
    • Authors: Huaying Huang; Boyong Long
      Pages: 121 - 127
      Abstract: Abstract Any Beltrami coefficient \(\mu \) on R represents a point \([\mu ]_T\) in Teichmüller space T(R) of a hyperbolic Riemann surface R and a point \([\mu ]_B\) in the tangent space of T(R) at the base point. The problem is whether \(\mu \) represents a Strebel point is equivalent to \(\mu \) represents an infinitesimal Strebel point. We prove that for any \(\mu \) , there exists an element \(\nu \) , such that \([\nu ]_T=[\mu ]_T\) and \([\nu ]_B\) is an infinitesimal Strebel point, when R is the unit disk.
      PubDate: 2017-03-01
      DOI: 10.1007/s40315-016-0171-1
      Issue No: Vol. 17, No. 1 (2017)
  • Frequently Hypercyclic Taylor Shifts
    • Authors: Maike Thelen
      Pages: 129 - 138
      Abstract: Abstract It is known that unimodular eigenvalues of an operator can give information about its dynamical behaviour. Recently, some situations have been characterized in which the Taylor shift operator is hypercyclic. The aim of this article is to use an eigenvalue criterion to find assumptions that guarantee the frequent hypercyclicity of the Taylor shift operator. As a conclusion, we also obtain holomorphic functions with smooth boundary values.
      PubDate: 2017-03-01
      DOI: 10.1007/s40315-016-0173-z
      Issue No: Vol. 17, No. 1 (2017)
  • A New Lower Bound for the Maximal Valence of Harmonic Polynomials
    • Authors: Seung-Yeop Lee; Andres Saez
      Pages: 139 - 149
      Abstract: Abstract We find a new lower bound for the maximal number of zeros of harmonic polynomials, \(p(z)+\overline{q(z)}\) , when \(\deg p = n\) and \(\deg q = n-2\) .
      PubDate: 2017-03-01
      DOI: 10.1007/s40315-016-0175-x
      Issue No: Vol. 17, No. 1 (2017)
  • Properties and Examples of Faber–Walsh Polynomials
    • Authors: Olivier Sète; Jörg Liesen
      Pages: 151 - 177
      Abstract: Abstract The Faber–Walsh polynomials are a direct generalization of the (classical) Faber polynomials from simply connected sets to sets with several simply connected components. In this paper, we derive new properties of the Faber–Walsh polynomials, where we focus on results of interest in numerical linear algebra, and on the relation between the Faber–Walsh polynomials and the classical Faber and Chebyshev polynomials. Moreover, we present examples of Faber–Walsh polynomials for two real intervals as well as for some non-real sets consisting of several simply connected components.
      PubDate: 2017-03-01
      DOI: 10.1007/s40315-016-0176-9
      Issue No: Vol. 17, No. 1 (2017)
  • Uniqueness Theorems for Differential Polynomials Sharing a Small Function
    • Authors: Thi Hoai An Ta; Viet Phuong Nguyen
      Abstract: Abstract Consider meromorphic functions f,  g,  and \(\alpha ,\) where \(\alpha \) is a small function with respect to f and g. Let Q be a polynomial of one variable. We give suitable conditions on the degree of Q and on the number of zeros and the multiplicities of the zeros of \(Q'\) so as to be able to conclude uniqueness results if differential polynomials of the form \((Q(f))^{(k)}\) and \((Q(g))^{(k)}\) share \(\alpha \) counting multiplicities. We do not assume that Q has a large order zero, nor do we place restrictions on the zeros and poles of \(\alpha .\) Thus, our work improves on many prior results that either assume Q has a high order zero or place restrictions on the small function \(\alpha \) .
      PubDate: 2017-04-25
      DOI: 10.1007/s40315-017-0198-y
  • Angular Derivatives for Holomorphic Self-Maps of the Disk
    • Authors: Jochen Becker; Christian Pommerenke
      Abstract: Abstract Let the function \(\varphi \) be holomorphic in the unit disk \(\mathbb {D}\) and let \(\varphi (\mathbb {D})\subset \mathbb {D}\) . We consider points \(\zeta \in \partial \mathbb {D}\) where \(\varphi \) has an angular limit \(\varphi (\zeta )\in \partial \mathbb {D}\) and study the behaviour of \((\varphi (z)-\varphi (\zeta ))/(z-\zeta )\) as z tends to \(\zeta \) in various ways. In particular, there is a result connecting \( \varphi '(\zeta _{\nu }) \) and \( \varphi (\zeta _{\mu })-\varphi (\zeta _{\nu }) \) for three points \(\zeta _{\nu }\) . Expressed as a positive semidefinite quadratic form, this result could, perhaps, be generalized to n points \(\zeta _{\nu }\) .
      PubDate: 2017-04-24
      DOI: 10.1007/s40315-017-0199-x
  • Criteria for Bounded Valence of Harmonic Mappings
    • Authors: Juha-Matti Huusko; María J. Martín
      Abstract: Abstract In 1984, Gehring and Pommerenke proved that if the Schwarzian derivative S(f) of a locally univalent analytic function f in the unit disk was such that \(\limsup _{ z \rightarrow 1} S(f)(z) (1- z ^2)^2 < 2\) , then there would exist a positive integer N such that f takes every value at most N times. Recently, Becker and Pommerenke have shown that the same result holds in those cases when the function f satisfies that \(\limsup _{ z \rightarrow 1} f''(z)/f'(z) \, (1- z ^2)< 1\) . In this paper, we generalize these two criteria for bounded valence of analytic functions to the cases when f is only locally univalent and harmonic.
      PubDate: 2017-03-28
      DOI: 10.1007/s40315-017-0197-z
  • A Normality Criterion Corresponding to the Defect Relations
    • Authors: Andreas Schweizer
      Abstract: Abstract Let \(\mathcal{{F}}\) be a family of meromorphic functions on a domain D. We present a quite general sufficient condition for \(\mathcal{{F}}\) to be a normal family. This criterion contains many known results as special cases. The overall idea is that certain comparatively weak conditions on \(\mathcal{{F}}\) by local arguments lead to somewhat stronger conditions, which in turn lead to even stronger conditions on the limit function g in the famous Zalcman Lemma. Ultimately, the defect relations for g force normality of \(\mathcal{{F}}\) .
      PubDate: 2017-03-25
      DOI: 10.1007/s40315-017-0196-0
  • About the Cover: Lambert Series
    • Authors: Elias Wegert
      PubDate: 2017-02-20
      DOI: 10.1007/s40315-017-0193-3
  • Some Results on the Rational Bernstein–Markov Property in the
           Complex Plane
    • Authors: Federico Piazzon
      Abstract: Abstract The Bernstein–Markov property is an asymptotic quantitative assumption on the growth of uniform norms of polynomials or rational functions on a compact set with respect to \(L^2_\mu \) -norms, where \(\mu \) is a positive finite measure. We consider two variants of the Bernstein–Markov property for rational functions with restricted poles and compare them with the polynomial Bernstein–Markov property to find some sufficient conditions for the latter to imply the former. Moreover, we recover a sufficient mass-density condition for a measure to satisfy the rational Bernstein–Markov property on its support. Finally we present, as an application, a meromorphic \(L^2\) version of the Bernstein–Walsh Lemma.
      PubDate: 2017-02-11
      DOI: 10.1007/s40315-017-0194-2
  • Quotients of Hyperbolic Metrics
    • Authors: David Minda
      Abstract: Abstract In this paper, precise versions of several intuitive properties of quotients of hyperbolic metrics are established. Suppose that \(\Omega _j\) is a hyperbolic region in \(\mathbb {C}_\infty = \mathbb {C}\cup \{\infty \}\) with hyperbolic metric \(\lambda _j\) , \(j=1,2\) , and \(\Omega _1 \subsetneq \Omega _2\) . First, it is shown that \(\lambda _1/ \lambda _2 \approx 1\) on compact subsets of \(\Omega _1\) that are not too close to \(\partial \Omega _1\) . Second, \(\lambda _1/ \lambda _2 \approx 1\) when z is near \((\partial \Omega _1 \;\cap \; \partial \Omega _2 ) {\setminus } F_b\) , where \(F = \partial \Omega _1 \;\cap \;\Omega _2\) and \(F_b = {{\mathrm{cl}}}(F)\;\cap \;\Omega _2\) . The main tools used in establishing these results are sharp elementary bounds for \(\lambda _1(z)/ \lambda _2(z)\) in terms of the hyperbolic distance relative to \(\Omega _2\) from z to \(\partial \Omega _1 \;\cap \;\Omega _2\) that were first established and employed in complex dynamics.
      PubDate: 2017-02-11
      DOI: 10.1007/s40315-017-0195-1
  • Second Main Theorems for Meromorphic Mappings with Moving Hypersurfaces
           and a Uniqueness Problem
    • Authors: Duc Quang Si; Phuong An Do
      Abstract: Abstract In this article, we establish some new second main theorems for meromorphic mappings of \({\mathbb {C}}^m\) into \({\mathbb {P}}^{n}({\mathbb {C}})\) and moving hypersurfaces with truncated counting functions in the case where the meromorphic mappings may be algebraically degenerate. Our results are improvements of some recent results on second main theorem in the two cases of moving hyperplanes and of moving hypersurfaces. As an application, a unicity theorem for meromorphic mappings sharing moving hypersurfaces is given.
      PubDate: 2017-01-30
      DOI: 10.1007/s40315-017-0192-4
  • Convergence of Row Sequences of Simultaneous Padé-orthogonal
    • Authors: N. Bosuwan
      Abstract: Abstract In this paper, convergence theorems of row sequences of vector valued Padé-orthogonal approximants (simultaneous Padé-orthogonal approximants) corresponding to a measure supported on a general compact subset of the complex plane are proved. These theorems are natural extensions of Montessus de Ballore’s theorem for row sequences of (scalar) Padé-orthogonal approximants in Bosuwan et al. (Jaen J Approx 5:179–208, 2013).
      PubDate: 2017-01-30
      DOI: 10.1007/s40315-017-0190-6
  • Birkhoff–James Orthogonality and the Zeros of an Analytic Function
    • Authors: Raymond Cheng; Javad Mashreghi; William T. Ross
      Abstract: Abstract Bounds are obtained for the zeros of an analytic function on a disk in terms of the Taylor coefficients of the function. These results are derived using the notion of Birkhoff–James orthogonality in the sequence space \(\ell ^p\) with \(p \in (1, \infty )\) , along with an associated Pythagorean theorem. It is shown that these methods are able to reproduce, and in some cases sharpen, some classical bounds for the roots of a polynomial.
      PubDate: 2017-01-27
      DOI: 10.1007/s40315-017-0191-5
  • A Problem of Bombieri on Univalent Functions
    • Authors: D. Aharonov; D. Bshouty
      Pages: 677 - 688
      Abstract: Abstract The famous Bieberbach Conjecture from 1916 on the coefficients of normalized univalent functions defined in the unit disk (Bieberbach, S.-B. Preuss Akad Wiss 138:940–955, 1916) that was finally proved by de Branges (Acta Math 154:137–152, 1985) some 70 years later, diverted the attention of many complex analysts to other subjects. Those who continued to explore de Branges method and push it as far as possible were not aware of where it may lead. Surprisingly enough, a paper that fell in our hands (Dong Acta Sci Nat Univ Norm Hunan 14:193–197, 1991) contained a way to tackle one of the problems of Bombieri (Research problems in function theory, The Athlone Press, University of London, London, 1967) on the behavior of the coefficients of univalent functions. We shall give an account of the history of the problem and a revised version of it.
      PubDate: 2016-12-01
      DOI: 10.1007/s40315-016-0165-z
      Issue No: Vol. 16, No. 4 (2016)
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