Authors:Asif R. Khan; Josip Pečarić; Marjan Praljak Pages: 881 - 889 Abstract: We give an integral version and a refinement of M. Niezgoda’s extension of the variant of Jensen’s inequality given by A. McD. Mercer. PubDate: 2017-04-01 DOI: 10.1007/s40840-017-0449-0 Issue No:Vol. 40, No. 2 (2017)

Authors:Xun-Hua Gong; Fang Liu Pages: 919 - 929 Abstract: In this paper, we consider of finding efficient solution and weakly efficient solution for nonconvex vector optimization problems. When X and Y are normed spaces, F is an anti-Lipschitz mapping from X to Y, and the ordering cone is regular, we present an algorithm to guarantee that the generated sequence converges to an efficient solution with respect to normed topology. If the domain of the mapping is compact, we prove that the generated sequence converges to an efficient solution with respect to normed topology without requiring that mapping is anti-Lipschitz. We also give an algorithm to guarantee that the generated sequence converges to a weakly efficient solution with respect to normed topology. PubDate: 2017-04-01 DOI: 10.1007/s40840-017-0455-2 Issue No:Vol. 40, No. 2 (2017)

Authors:K. Teerapabolarn Pages: 931 - 939 Abstract: The Stein–Chen method is used to determine uniform and non-uniform bounds on the ratio between the distribution function of a sum of independent negative binomial random variables and a Poisson distribution function with mean \(\lambda = \sum _{i=1}^nr_iq_i\) , where \(r_i\) and \(p_i=1-q_i\) are parameters of each negative binomial distribution. With these bounds, it indicates that the Poisson distribution function with this mean can be used as an estimate of the independent summands when all \(q_i\) are small or \(\lambda \) is small. Finally, some numerical examples for each result are given. PubDate: 2017-04-01 DOI: 10.1007/s40840-016-0328-0 Issue No:Vol. 40, No. 2 (2017)

Authors:Sameerah Jamal; A. Mathebula Abstract: This paper considers different routes to generalized symmetries for some ecological equations that arise in spatial theory. Two primary methods for the derivation of generalized symmetries are the standard Lie invariance condition with vector fields dependent on derivatives and, secondly, a recursive operator. The former is less efficient especially if it includes derivatives that become increasingly higher in order, and this necessarily complicates the nature of the computations. The latter involves a nontrivial analysis to define a recursion operator, if one exists, but is successful in providing higher-order analogs of the equation or equivalently, higher-order symmetries. A linear Kierstead–Slobodkin and Skellam model is shown to possess a recursion operator that renders the equation completely integrable, by verifying the presence of infinitely many higher-order symmetries. Moreover, we apply the scheme of the characteristic approach to establish nontrivial conserved vectors from multipliers \({\varLambda }(t,x,u,u_x,u_t),\) that are analogous to integrating factors. PubDate: 2017-05-20 DOI: 10.1007/s40840-017-0510-z

Authors:Caisheng Chen; Hongwei Yang Abstract: In this work the symmetric mountain pass lemma is employed to establish the existence of infinitely many solutions for a class of quasilinear Schrödinger system in \({\mathbb {R}}^{N}\) involving a parameter \(\alpha \) and subcritical nonlinearities. PubDate: 2017-05-15 DOI: 10.1007/s40840-017-0502-z

Authors:M. Mursaleen; Khursheed J. Ansari Abstract: In the present paper, we introduce a two parametric q-analogue of Stancu-Beta operators and establish some direct results in the polynomial weighted space of continuous functions defined on the interval \([0,\infty )\) . We use Lipschitz-type maximal function to find pointwise estimate. Furthermore, we obtain a Voronovskaja-type theorem for these operators. PubDate: 2017-05-12 DOI: 10.1007/s40840-017-0499-3

Authors:Dawood Hassanzadeh-Lelekaami; Hajar Roshan-Shekalgourabi Abstract: In this paper, we investigate the class of von Neumann regular modules over commutative rings. More precisely, we introduce a characterization of regular modules, and then, we study some properties of these modules in viewpoint of this characterization. Among other things, we show that the Nakayama’s Lemma and Krull’s intersection theorem hold for this class of modules. Also, some explicit expressions for submodules of regular modules are introduced. PubDate: 2017-05-12 DOI: 10.1007/s40840-017-0501-0

Authors:Juan de Dios Pérez; Changhwa Woo Abstract: We prove the nonexistence of Hopf real hypersurfaces in complex two-plane Grassmannians such that the covariant derivatives with respect to Levi-Civita and kth generalized Tanaka–Webster connections in the direction of the Reeb vector field applied to the Riemannian curvature tensor coincide when the shape operator and the structure operator commute on the \(\mathcal Q\) -component of the Reeb vector field. PubDate: 2017-05-08 DOI: 10.1007/s40840-017-0500-1

Authors:Seung Jun Chang; Jae Gil Choi; Il Yong Lee Abstract: In this paper, we use a generalized Brownian motion process to define an analytic operator-valued Feynman integral. We then establish the existence of the analytic operator-valued generalized Feynman integral. We next investigate a stability theorem for the analytic operator-valued generalized Feynman integral. PubDate: 2017-05-03 DOI: 10.1007/s40840-017-0498-4

Authors:Phan Quoc Khanh; Nguyen Hong Quan Abstract: We prove a topologically based characterization of the existence of fixed-component points for an arbitrary family of set-valued maps defined on a product set by using topologically based structures, without linear or convexity structures. Then, applying this general result, we derive sufficient conditions for the existence of coincidence-component points of families of set-valued maps and intersection points of families of sets, as examples for many other important points in nonlinear analysis. Applications to systems of variational relations and abstract economies are provided as examples for other optimization-related problems. PubDate: 2017-05-02 DOI: 10.1007/s40840-017-0496-6

Authors:Shoufeng Wang Abstract: As generalizations of inverse semigroups, restriction semigroups and regular \(*\) -semigroups are investigated by many authors extensively in the literature. In particular, Lawson and Hollings have proved that the category of restriction semigroups together with prehomomorphisms (resp. (2,1,1)-homomorphisms) is isomorphic to the category of inductive categories together with ordered functors (resp. strongly ordered functors), which generalizes the well-known Ehresmann–Schein–Nambooripad theorem (ESN theorem for short) for inverse semigroups. On the other hand, Imaoka and Fujiwara have also obtained an ESN-type theorem for locally inverse regular \(*\) -semigroups. Recently, Jones generalized restriction semigroups and regular \(*\) -semigroups to P-restriction semigroups from a varietal perspective and considered the constructions of P-restriction semigroups by using Munn’s approach. In this paper, we shall study the class of P-restriction semigroups by using “category approach.” We introduce the notion of inductive generalized categories over local semilattices by which a class of P-restriction semigroups called locally restriction P-restriction semigroups is described. Moreover, we show that the category of locally restriction P-restriction semigroups together with (2,1,1)-prehomomorphisms (resp. (2,1,1)-homomorphisms) is isomorphic to the category of inductive generalized categories over local semilattices together with preadmissible mappings (resp. admissible mappings). Our work may be regarded as extending the ESN-type theorems for restriction semigroups and locally inverse regular \(*\) -semigroups, respectively. PubDate: 2017-05-02 DOI: 10.1007/s40840-017-0497-5

Authors:W. M. Abd-Elhameed Abstract: In this article, some new efficient and accurate algorithms are developed for solving linear and nonlinear odd-order two-point boundary value problems. The algorithm in linear case is based on the application of Petrov–Galerkin method. For implementing this algorithm, two certain families of generalized Jacobi polynomials are introduced and employed as trial and test functions. The trial functions satisfy the underlying boundary conditions of the differential equations, and the test functions satisfy the dual boundary conditions. The developed algorithm leads to linear systems with band matrices which can be efficiently inverted. These special systems are carefully investigated, especially their complexities. Another algorithm based on the application of the typical collocation method is presented for handling nonlinear odd-order two-point boundary value problems. The use of generalized Jacobi polynomials leads to simplified analysis and very efficient numerical algorithms. Numerical results are presented for the sake of testing the efficiency and applicability of the two proposed algorithms. PubDate: 2017-04-27 DOI: 10.1007/s40840-017-0491-y

Authors:Qinghua Hu; Songxiao Li; Hasi Wulan Abstract: In this paper, we give some new essential norm estimates of weighted composition operators \(uC_{\varphi }\) from analytic Besov spaces into the Bloch space, where u is a function analytic on the unit disk \(\mathbb {D}\) and \(\varphi \) is an analytic self-map of \(\mathbb {D}\) . Moreover, new characterizations for the boundedness, compactness and essential norm of weighted composition operators \(uC_{\varphi }\) are obtained by the nth power of the symbol \(\varphi \) and the Volterra operators \(I_u\) and \(J_u\) . PubDate: 2017-04-21 DOI: 10.1007/s40840-017-0493-9

Authors:Nguyen Van Thin Abstract: In this paper, we study the value distribution of differential polynomial with the form \(f^n(f^{n_1})^{(t_1)}\dots (f^{n_k})^{(t_k)},\) where f is a transcendental meromorphic function. Namely, we prove that \(f^n(f^{n_1})^{(t_1)}\dots (f^{n_k})^{(t_k)}-P(z)\) has infinitely zeros, where P(z) is a nonconstant polynomial and \(n\in {\mathbb {N}},\) \(k, n_1, \dots , n_k, t_1, \dots , t_k\) are positive integer numbers satisfying \(n+\sum _{v}^{k}n_v\ge \sum _{v=1}^{k}t_v+3.\) Using it, we establish some normality criterias for family of meromorphic functions under a condition where differential polynomials generated by the members of the family share a holomorphic function with zero points. Our results generalize some previous results on normal family of meromorphic functions. PubDate: 2017-04-21 DOI: 10.1007/s40840-017-0492-x

Authors:Pham Thanh Hieu; Nguyen Thi Thu Thuy; Jean Jacques Strodiot Abstract: The problem of finding a solution of a variational inequality over the set of common fixed points of a nonexpansive semigroup is considered in a real and uniformly convex Banach space without imposing the sequential weak continuity of the normalized duality mapping. Two new explicit iterative methods are introduced based on the steepest-descent method, and conditions are given to obtain their strong convergence. A numerical example is showed to illustrate the convergence analysis of the proposed methods. PubDate: 2017-04-20 DOI: 10.1007/s40840-017-0494-8

Authors:Yong Zhou; Bashir Ahmad; Fulai Chen; Ahmed Alsaedi Abstract: In this paper, we develop the sufficient criteria for the oscillation of all solutions to the following fractional functional partial differential equation involving Riemann–Liouville fractional derivative equipped with initial and Neumann, Dirichlet and Robin boundary conditions: 1.1 $$\begin{aligned} \displaystyle \frac{\partial ^{\alpha } u(x, t)}{\partial t^{\alpha }}=C(t)\triangle u+\displaystyle \sum \limits _{i=1}^{n}P_i(x)u(x, t-\sigma _i)+R(x, t), \end{aligned}$$ where \(0<\alpha <1\) , \((x, t)\in \Omega \times (0, \infty )\) , \(\Omega \) is a bounded domain in Euclidean \(n-\) dimensional space \(\mathbb {R}^n\) with a piecewise smooth boundary \(\partial \Omega \) ; \(C\in C((0,\infty ),(-\infty ,0]),\) \(\triangle \) is the Laplacian in \(\mathbb {R}^\texttt {n}, P_i\in C(\Omega ,[0,\infty )), R(x,t)\in C(G, (-\infty ,\infty )), \sigma _i\in [0,\infty ), i=1,2,\ldots ,n\) . PubDate: 2017-04-20 DOI: 10.1007/s40840-017-0495-7

Authors:LeRoy B. Beasley; Preeti Mohindru; Rajesh Pereira Abstract: A real symmetric matrix A is called completely positive if there exists a nonnegative real \(n\times k\) matrix B such that \(A = BB^{t}\) . The smallest value of k for all possible choices of nonnegative matrices B is called the CP-rank of A. We extend the ideas of complete positivity and the CP-rank to matrices whose entries are elements of an incline in a similar way. We classify maps on the set of \(n \times n\) symmetric matrices over certain inclines which strongly preserve CP-rank-1 matrices as well as maps which preserve CP-rank-1 and CP-rank-k. The result suggests that there is a certain standard class of solutions for CP-rank preserver problems on incline matrices. PubDate: 2017-04-18 DOI: 10.1007/s40840-017-0490-z

Authors:Qiaojun Shu; Yiqiao Wang; Yulai Ma; Weifan Wang Abstract: A proper edge coloring is called acyclic if no bichromatic cycles are produced. It was conjectured that every simple graph G with maximum degree \(\varDelta \) is acyclically edge- \((\varDelta +2)\) -colorable. Basavaraju and Chandran (J Graph Theory 61:192–209, 2009) confirmed the conjecture for non-regular graphs G with \(\varDelta =4\) . In this paper, we extend this result by showing that every 4-regular graph G without 3-cycles is acyclically edge-6-colorable. PubDate: 2017-04-09 DOI: 10.1007/s40840-017-0484-x

Authors:H. M. Barakat; E. M. Nigm; A. H. Syam Abstract: We introduce the Huang–Kotz Morgenstern type bivariate generalized exponential distribution. Some distributional properties of concomitants of order statistics as well as record values for this family are studied. Recurrence relations between single and product moments of concomitants are obtained. Moreover, the rank and the asymptotic behavior of concomitants of order statistics are investigated. PubDate: 2017-04-05 DOI: 10.1007/s40840-017-0489-5

Abstract: Given a positive integer t and a graph F, the goal is to assign a subset of the color set \(\{1,2,\ldots ,t\}\) to every vertex of F such that every vertex with the empty set assigned has all t colors in its neighborhood. Such an assignment is called the t-rainbow dominating function ( \(t\mathrm{RDF}\) ) of the graph F. A \(t\mathrm{RDF}\) is independent ( \(It\mathrm{RDF}\) ) if vertices assigned with non-empty sets are pairwise non-adjacent. The weight of a \(t\mathrm{RDF}\) g of a graph F is the value \(w(g) =\sum _{v \in V(F)} g(v) \) . The independent t-rainbow domination number \(i_{rt}(F)\) is the minimum weight over all \(It\mathrm{RDF}\) s of F. In this article, it is proved that the independent t-rainbow domination problem is NP-complete even if the input graph is restricted to a bipartite graph or a planar graph, and the results of the study provide some bounds for the independent t-rainbow domination number of any graph for a positive integer t. Moreover, the exact values and bounds of the independent t-rainbow domination numbers of some Petersen graphs and torus graphs are given. PubDate: 2017-04-04 DOI: 10.1007/s40840-017-0488-6