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Publisher: Springer-Verlag (Total: 2350 journals)

 Aequationes MathematicaeJournal Prestige (SJR): 0.517 Citation Impact (citeScore): 1Number of Followers: 2      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1420-8903 - ISSN (Online) 0001-9054 Published by Springer-Verlag  [2350 journals]
• Mappings of preserving n -distance one in n -normed spaces
• Authors: Xujian Huang; Dongni Tan
Pages: 401 - 413
Abstract: We give a positive answer to the Aleksandrov problem in n-normed spaces under the surjectivity assumption. Namely, we show that every surjective mapping preserving n-distance one is affine, and thus is an n-isometry. This is the first time the Aleksandrov problem is solved in n-normed spaces with only the surjectivity assumption even in the usual case $$n=2$$ . Finally, when the target space is n-strictly convex, we prove that every mapping preserving two n-distances with an integer ratio is an affine n-isometry.
PubDate: 2018-06-01
DOI: 10.1007/s00010-018-0539-6
Issue No: Vol. 92, No. 3 (2018)

• Groups with a ternary equivalence relation
• Authors: Helmut Karzel; Sayed-Ghahreman Taherian
Pages: 415 - 423
Abstract: We consider in a group $$(G,\cdot )$$ the ternary relation \begin{aligned} \kappa := \{(\alpha , \beta , \gamma ) \in G^3 \ \ \alpha \cdot \beta ^{-1} \cdot \gamma = \gamma \cdot \beta ^{-1} \cdot \alpha \} \end{aligned} and show that $$\kappa$$ is a ternary equivalence relation if and only if the set $$\mathfrak Z$$ of centralizers of the group G forms a fibration of G (cf. Theorems 2, 3). Therefore G can be provided with an incidence structure \begin{aligned} \mathfrak G:= \{\gamma \cdot Z \ \ \gamma \in G , Z \in \mathfrak Z(G) \}. \end{aligned} We study the automorphism group of $$(G,\kappa )$$ , i.e. all permutations $$\varphi$$ of the set G such that $$(\alpha , \beta , \gamma ) \in \kappa$$ implies $$(\varphi (\alpha ),\varphi (\beta ),\varphi (\gamma ))\in \kappa$$ . We show $$\mathrm{Aut}(G,\kappa )=\mathrm{Aut}(G,\mathfrak G)$$ , $$\mathrm{Aut} (G,\cdot ) \subseteq \mathrm{Aut}(G,\kappa )$$ and if $$\varphi \in \mathrm{Aut}(G,\kappa )$$ with $$\varphi (1)=1$$ and $$\varphi (\xi ^{-1})= (\varphi (\xi ))^{-1}$$ for all $$\xi \in G$$ then $$\varphi$$ is an automorphism of $$(G,\cdot )$$ . This allows us to prove a representation theorem of $$\mathrm{Aut}(G,\kappa )$$ (cf. Theorem 6) and that for $$\alpha \in G$$ the maps \begin{aligned} \tilde{\alpha }\ : \ G \rightarrow G;~ \xi \mapsto \alpha \cdot \xi ^{-1} \cdot \alpha \end{aligned} of the corresponding reflection structure $$(G, \widetilde{G})$$ (with $$\tilde{G} := \{\tilde{\gamma }\ \ \gamma \in G \}$$ ) are point reflections. If $$(G ,\cdot )$$ is uniquely 2-divisible and if for $$\alpha \in G$$ , $$\alpha ^{1\over 2}$$ denotes the unique solution of $$\xi ^2=\alpha$$ then with $$\alpha \odot \beta := \alpha ^{1\over 2} \cdot \beta \cdot \alpha ^{1\over 2}$$ , the pair
PubDate: 2018-06-01
DOI: 10.1007/s00010-018-0543-x
Issue No: Vol. 92, No. 3 (2018)

• Redheffer type bounds for Bessel and modified Bessel functions of the
first kind
• Authors: Árpád Baricz; Khaled Mehrez
Pages: 425 - 439
Abstract: In this paper our aim is to show some new inequalities of the Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series. We also use some known results on the quotients of Bessel and modified Bessel functions of the first kind, and by using the monotonicity of the Dirichlet eta function we prove a sharp inequality for the tangent function. At the end of the paper a conjecture is stated, which may be of interest for further research.
PubDate: 2018-06-01
DOI: 10.1007/s00010-018-0545-8
Issue No: Vol. 92, No. 3 (2018)

• Polynomials whose coefficients coincide with their zeros
• Authors: Oksana Bihun; Damiano Fulghesu
Pages: 453 - 470
Abstract: In this paper we consider monic polynomials such that their coefficients coincide with their zeros. These polynomials were first introduced by S. Ulam. We combine methods of algebraic geometry and dynamical systems to prove several results. We obtain estimates on the number of Ulam polynomials of degree N. We provide additional methods to obtain algebraic identities satisfied by the zeros of Ulam polynomials, beyond the straightforward comparison of their zeros and coefficients. To address the question about the existence of orthogonal Ulam polynomial sequences, we show that the only Ulam polynomial eigenfunctions of hypergeometric type differential operators are the trivial Ulam polynomials $$\{x^N\}_{N=0}^\infty$$ . We propose a family of solvable N-body problems such that their stable equilibria are the zeros of certain Ulam polynomials.
PubDate: 2018-06-01
DOI: 10.1007/s00010-018-0546-7
Issue No: Vol. 92, No. 3 (2018)

• On functional equations stemming from actuarial mathematics
• Authors: Jacek Chudziak
Pages: 471 - 486
Abstract: We determine extensions of some implicitly defined functionals stemming from actuarial mathematics.
PubDate: 2018-06-01
DOI: 10.1007/s00010-017-0519-2
Issue No: Vol. 92, No. 3 (2018)

• On k -additive uniqueness of the set of squares for multiplicative
functions
• Authors: Poo-Sung Park
Pages: 487 - 495
Abstract: P. V. Chung showed that there are many multiplicative functions f which satisfy $$f(m^2+n^2) = f(m^2)+f(n^2)$$ for all positive integers m and n. In this article, we show that if more than 2 squares in the additive condition are involved, then such f is uniquely determined. That is, if a multiplicative function f satisfies \begin{aligned} f(a_1^2 + a_2^2 + \cdots + a_k^2) = f(a_1^2) + f(a_2^2) + \cdots + f(a_k^2) \end{aligned} for arbitrary positive integers $$a_i$$ , then f is the identity function. In this sense, we call the set of all positive squares a k-additive uniqueness set for multiplicative functions.
PubDate: 2018-06-01
DOI: 10.1007/s00010-017-0517-4
Issue No: Vol. 92, No. 3 (2018)

• Packing chromatic number versus chromatic and clique number
• Authors: Boštjan Brešar; Sandi Klavžar; Douglas F. Rall; Kirsti Wash
Pages: 497 - 513
Abstract: The packing chromatic number $$\chi _{\rho }(G)$$ of a graph G is the smallest integer k such that the vertex set of G can be partitioned into sets $$V_i$$ , $$i\in [k]$$ , where each $$V_i$$ is an i-packing. In this paper, we investigate for a given triple (a, b, c) of positive integers whether there exists a graph G such that $$\omega (G) = a$$ , $$\chi (G) = b$$ , and $$\chi _{\rho }(G) = c$$ . If so, we say that (a, b, c) is realizable. It is proved that $$b=c\ge 3$$ implies $$a=b$$ , and that triples $$(2,k,k+1)$$ and $$(2,k,k+2)$$ are not realizable as soon as $$k\ge 4$$ . Some of the obtained results are deduced from the bounds proved on the packing chromatic number of the Mycielskian. Moreover, a formula for the independence number of the Mycielskian is given. A lower bound on $$\chi _{\rho }(G)$$ in terms of $$\Delta (G)$$ and $$\alpha (G)$$ is also proved.
PubDate: 2018-06-01
DOI: 10.1007/s00010-017-0520-9
Issue No: Vol. 92, No. 3 (2018)

• A comprehensive study of $${\varvec{r}}$$ r -Dowling polynomials
• Authors: Eszter Gyimesi; Gábor Nyul
Pages: 515 - 527
Abstract: After his extensive study of Whitney numbers, Benoumhani introduced Dowling numbers and polynomials as generalizations of the well-known Bell numbers and polynomials. Later, Cheon and Jung gave the r-generalization of these notions. Based on our recent combinatorial interpretation of r-Whitney numbers, in this paper we derive several new properties of r-Dowling polynomials and we present alternative proofs of some previously known ones.
PubDate: 2018-06-01
DOI: 10.1007/s00010-017-0538-z
Issue No: Vol. 92, No. 3 (2018)

• Inscribed and circumscribed polygons that characterize inner product
spaces
• Authors: Carlos Benítez; Pedro Martín; Diego Yáñez
Pages: 529 - 541
Abstract: Let X be a real normed space with unit sphere S. We prove that X is an inner product space if and only if there exists a real number $$\rho =\sqrt{(1+\cos \frac{2k\pi }{2m+1})/2}, (k=1,2,\ldots ,m; m=1,2,\ldots )$$ , such that every chord of S that supports $$\rho S$$ touches $$\rho S$$ at its middle point. If this condition holds, then every point $$u\in S$$ is a vertex of a regular polygon that is inscribed in S and circumscribed about $$\rho S$$ .
PubDate: 2018-06-01
DOI: 10.1007/s00010-018-0540-0
Issue No: Vol. 92, No. 3 (2018)

• On the alienation of the logarithmic and exponential Cauchy equations
• Authors: Gyula Maksa
Pages: 543 - 547
Abstract: In this paper, we give the solution of a problem formulated in Kominek and Sikorska (Aequationes Math 90:107–121, 2016) in connection with the functional equation \begin{aligned} f(xy)-f(x)-f(y)=g(x+y)-g(x)g(y). \end{aligned} Our result can also be interpreted in the way that, under some additional condition, the logarithmic and the exponential Cauchy equations are strongly alien.
PubDate: 2018-06-01
DOI: 10.1007/s00010-017-0535-2
Issue No: Vol. 92, No. 3 (2018)

• Disjointness preserving maps between vector-valued group algebras
• Authors: Maliheh Hosseini; Juan J. Font
Pages: 549 - 561
Abstract: Let G be a locally compact abelian group and B be a commutative Banach algebra. Let $$L^{1}(G, B)$$ be the Banach algebra of B-valued Bochner integrable functions on G. In this paper we provide a complete description of continuous disjointness preserving maps on $$L^{1}(G, B)$$ -algebras based on a scarcely used tool: the vector-valued Fourier transform. We also present necessary and sufficient conditions for these operators to be compact.
PubDate: 2018-06-01
DOI: 10.1007/s00010-018-0547-6
Issue No: Vol. 92, No. 3 (2018)

• Algebraic conditions for additive functions over the reals and over finite
fields
• Authors: Péter Kutas
Pages: 563 - 575
Abstract: Let C be an affine plane curve. We consider additive functions $$f{:}\; K\rightarrow K$$ for which $$f(x)f(y)=0$$ , whenever $$(x,y)\in C$$ . We show that if $$K=\mathbb {R}$$ and C is the hyperbola with defining equation $$xy=1$$ , then there exist nonzero additive functions with this property. Moreover, we show that such a nonzero f exists for a field K if and only if K is transcendental over $$\mathbb Q$$ or over $$\mathbb {F}_p$$ , the finite field with p elements. We also consider the general question when K is a finite field. We show that if the degree of the curve C is large enough compared to the characteristic of K, then f must be identically zero.
PubDate: 2018-06-01
DOI: 10.1007/s00010-017-0521-8
Issue No: Vol. 92, No. 3 (2018)

• Authors: Bruce Ebanks
Pages: 581 - 597
Abstract: We continue the study of additive functions $$f_k:R\rightarrow F \;(1\le k\le n)$$ linked by an equation of the form $$\sum _{k=1}^n p_k(x)f_k(q_k(x))=0$$ , where the $$p_k$$ and $$q_k$$ are polynomials, R is an integral domain of characteristic 0, and F is the fraction field of R. A method is presented for solving all such equations. We also consider the special case $$\sum _{k=1}^n x^{m_k}f_k(x^{j_k})=0$$ in which the $$p_k$$ and $$q_k$$ are monomials. In this case we show that if there is no duplication, i.e. if $$(m_k,j_k)\ne (m_p,j_p)$$ for $$k\ne p$$ , then each $$f_k$$ is the sum of a linear function and a derivation of order at most $$n-1$$ . Furthermore, if this functional equation is not homogeneous then the maximal orders of the derivations are reduced in a specified way.
PubDate: 2018-06-01
DOI: 10.1007/s00010-017-0537-0
Issue No: Vol. 92, No. 3 (2018)

• On a transport problem and monoids of non-negative integers
• Authors: Aureliano M. Robles-Pérez; José Carlos Rosales
Abstract: A problem about how to transport profitably a group of cars leads us to studying the set T formed by the integers n such that the system of inequalities, with non-negative integer coefficients, \begin{aligned} a_1x_1 +\cdots + a_px_p + \alpha \le n \le b_1x_1 +\cdots + b_px_p - \beta \end{aligned} has at least one solution in $${\mathbb N}^p$$ . We prove that $$T\cup \{0\}$$ is a submonoid of $$({\mathbb N},+)$$ and, moreover, we give algorithmic processes to compute T.
PubDate: 2018-06-05
DOI: 10.1007/s00010-018-0572-5

• Functions generating ( m,M, $$\varvec{\Psi }$$ Ψ )-Schur-convex sums
• Abstract: The notion of $$(m,M,\Psi )$$ -Schur-convexity is introduced and functions generating $$(m,M,\Psi )$$ -Schur-convex sums are investigated. An extension of the Hardy–Littlewood–Pólya majorization theorem is obtained. A counterpart of the result of Ng stating that a function generates $$(m,M,\Psi )$$ -Schur-convex sums if and only if it is $$(m,M,\psi )$$ -Wright-convex is proved and a characterization of $$(m,M,\psi )$$ -Wright-convex functions is given.
PubDate: 2018-05-30
DOI: 10.1007/s00010-018-0569-0

• On mappings which approximately preserve angles
• Abstract: In this paper, we study mappings, which approximately preserve angles between inner product spaces. We also introduce a notion of angle in normed spaces. The notion of angle, considered in this part, relates to the well-known Birkhoff–James orthogonality. Based on it, we express a characterization for approximate Birkhoff–James orthogonality, introduced in the literature, through this notion of angle. Then we return to the issue of mappings which approximately preserve angle stating some results in normed spaces.
PubDate: 2018-05-30
DOI: 10.1007/s00010-018-0571-6

• The CMP inverse for rectangular matrices
• Authors: Dijana Mosić
Abstract: We extend the notation of the CMP inverse for a square matrix to a rectangular matrix. Precisely, we define and characterize a new generalized inverse called the weighted CMP inverse. Also, we investigate properties of the weighted CMP inverse using a representation by block matrices. Some new characterizations and properties of the CMP inverse are obtained.
PubDate: 2018-05-14
DOI: 10.1007/s00010-018-0570-7

• Correction to: On generalized Rubel’s equation
• Authors: S. S. Linchuk; Yu. S. Linchuk
Abstract: In the original publication linking to CrossRef, MATH, MathSciNet were missed for the References [9–12]. The correct References are given below.
PubDate: 2018-03-30
DOI: 10.1007/s00010-018-0551-x

• An elementary proof for the majorization principle for Wright-convex
functions
• Authors: Mihai Monea; Dan Ştefan Marinescu
Abstract: We give another elementary proof for the majorization principle for Wright-convex functions. This inequality is due to Ng.
PubDate: 2018-03-30
DOI: 10.1007/s00010-018-0549-4

• Functional equations involving Sibuya’s dependence function
• Authors: Nikolai Kolev; Jayme Pinto
Abstract: We introduce a new probability aging notion via a functional equation based on the tail invariance of Sibuya’s dependence function which is specified as the ratio between the joint survival function and the product of its marginal survival functions. Solutions of the functional equation are generated by Gumbel’s type I bivariate exponential distribution and independence law. In a particular setting, we construct a version of Gumbel’s law with a singular component.
PubDate: 2018-03-28
DOI: 10.1007/s00010-018-0544-9

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