Authors:Flavia-Corina Mitroi-Symeonidis; Nicuşor Minculete Pages: 311 - 319 Abstract: In this note we describe some results concerning upper and lower bounds for the Jensen functional. We use several known and new results to shed light on the concept of a strongly convex function. PubDate: 2018-01-01 DOI: 10.1007/s40840-015-0293-z Issue No:Vol. 41, No. 1 (2018)

Authors:H. Amraei; H. R. Maimani; M. R. Pournaki; A. Zaeembashi Pages: 321 - 334 Abstract: Let R be a finite commutative ring with nonzero identity and denote its Jacobson radical by J(R). The Jacobson graph of R is the graph in which the vertex set is \(R\setminus J(R)\) , and two distinct vertices x and y are adjacent if and only if \(1-xy\) is not a unit in R. In this paper, up to isomorphism, we classify the rings R whose Jacobson graphs are toroidal. PubDate: 2018-01-01 DOI: 10.1007/s40840-015-0294-y Issue No:Vol. 41, No. 1 (2018)

Authors:Pei-Chu Hu; Qiong Wang Abstract: Take complex numbers \(\alpha ,\beta ,c,a_j,b_j\) \((j=0,1,2)\) such that \(c\ne 0\) and $$\begin{aligned} \mathrm{rank} \left( \begin{array}{ccc} a_{0} &{} a_{1} &{} a_{2}\\ b_{0} &{} b_{1} &{} b_{2}\\ \end{array} \right) =2. \end{aligned}$$ We show that if the following functional equation of Fermat type $$\begin{aligned} \begin{aligned} \left\{ a_{0}f(z)+a_{1}f(z+c)+a_{2}f'(z)\right\} ^3+\left\{ b_{0}f(z)+b_{1}f(z+c)+b_{2}f'(z)\right\} ^3=e^{\alpha z+\beta } \end{aligned} \end{aligned}$$ has meromorphic solutions of finite order, then it has only entire solutions of the form \(f(z)=Ae^{\frac{\alpha z+\beta }{3}}+Ce^{Dz},\) where A, C, D are constants, which generalizes some results due to Han and Lü. PubDate: 2018-02-23 DOI: 10.1007/s40840-018-0613-1

Authors:Phikul Sridarat; Raweerote Suparaturatorn; Suthep Suantai; Yeol Je Cho Abstract: In this paper, we prove weak and strong convergence theorems of SP-iteration for common fixed point of three G-nonexpansive mappings in uniformly convex Banach spaces endowed with a directed graph under some suitable control conditions. We also give some numerical examples for confirming our main theorem and compare convergence rate between SP-iteration and Noor iteration. PubDate: 2018-02-19 DOI: 10.1007/s40840-018-0606-0

Authors:Gabriel A. Barragán-Ramírez; Alejandro Estrada-Moreno; Yunior Ramírez-Cruz; Juan A. Rodríguez-Velázquez Abstract: The metric dimension is quite a well-studied graph parameter. Recently, the local metric dimension and the adjacency dimension have been introduced and studied. In this paper, we give a general formula for the local metric dimension of the lexicographic product \(G \circ \mathcal {H}\) of a connected graph G of order n and a family \(\mathcal {H}\) composed of n graphs. We show that the local metric dimension of \(G \circ \mathcal {H}\) can be expressed in terms of the numbers of vertices in the true twin equivalence classes of G, and the local adjacency dimension of the graphs in \(\mathcal {H}\) . PubDate: 2018-02-19 DOI: 10.1007/s40840-018-0611-3

Authors:Uǧur Kadak; H. M. Srivastava; M. Mursaleen Abstract: In the present paper, we introduce the notion of relatively uniform weighted summability and its statistical version based upon fractional-order difference operators of functions. The concept of relatively uniform weighted \(\alpha \beta \) -statistical convergence is also introduced and some inclusion relations concerning the newly proposed methods are derived. As an application, we prove a general Korovkin-type approximation theorem for functions of two variables and also construct an illustrative example by the help of generating function type non-tensor Meyer-König and Zeller operators. Moreover, it is shown that the proposed methods are non-trivial generalizations of relatively uniform convergence which includes a scale function. We estimate the rate of convergence of approximating positive linear operators by means of the modulus of continuity and give a Voronovskaja-type approximation theorem. Finally, we present some computational results and geometrical interpretations to illustrate some of our approximation results. PubDate: 2018-02-19 DOI: 10.1007/s40840-018-0612-2

Authors:Sandi Klavžar; Paul Manuel Abstract: A recent variation of the classical geodetic problem, the strong geodetic problem, is defined as follows. If G is a graph, then \(\mathrm{sg}(G)\) is the cardinality of a smallest vertex subset S, such that one can assign a fixed geodesic to each pair \(\{x,y\}\subseteq S\) so that these \(\left( {\begin{array}{c} S \\ 2\end{array}}\right) \) geodesics cover all the vertices of G. In this paper, the strong geodetic problem is studied on Cartesian product graphs. A general upper bound is proved on the Cartesian product of a path with an arbitrary graph and showed that the bound is tight on thin grids and thin cylinders. PubDate: 2018-02-16 DOI: 10.1007/s40840-018-0609-x

Authors:Qingsen Xu; Jinchuan Hou Abstract: Let H be a complex Hilbert space with dim H \(\ge \) 3, \(\mathcal {B}_s(H)\) be the Jordan algebra of all bounded self-adjoint operators on H, and let \(F:B(H)\rightarrow [d,\infty ]\) with \(d\ge 0\) be a radial unitary similarity invariant function. In this paper, a characterization is obtained for maps \(\phi \) on \(\mathcal {B}_s(H)\) satisfying \(F(\phi (A)\phi (B)\phi (A))=F(ABA)\ \ (A,B\in \mathcal {B}_s(H))\) . As applications, a general form of the maps on \(\mathcal {B}_s(H)\) preserving the p-norm, the maps preserving the pseudo-spectral radius and the maps preserving the pseudo-spectrum are also described. PubDate: 2018-02-16 DOI: 10.1007/s40840-018-0610-4

Authors:Le A. Tuan; Vu N. Phat Abstract: This paper investigates the problem of finite-time stability and control for a class of nonlinear singular discrete-time neural networks with time-varying delays and disturbances. First, based on the implicit function theorem and singular value decomposition method, a sufficient condition for the existence of the solution of such systems is established in terms of a linear matrix inequality (LMI). Then, using the Lyapunov functional approach combined with LMI technique we provide new delay-dependent sufficient conditions for robust \(H_{\infty }\) finite-time stability and control. Finally, some numerical examples are given to illustrate the efficiency of the proposed results. PubDate: 2018-02-13 DOI: 10.1007/s40840-018-0608-y

Authors:Kaituo Liu; Weiwei Li; Tian Yue Abstract: In this paper, we investigate the Hardy–Lorentz–Karamata spaces for Banach space-valued martingales. Relying on the geometrical properties of the underlying Banach spaces, we establish the atomic decompositions and characterize the dual spaces of these spaces. We also obtain some martingale inequalities in the setting of Hardy–Lorentz–Karamata spaces. PubDate: 2018-02-12 DOI: 10.1007/s40840-018-0607-z

Authors:Rui-Ting Jiang; Chun-Lei Tang Abstract: In the present paper, we study the semilinear elliptic problem \(\displaystyle -\Delta u -\mu \frac{u}{ y ^{2}}=\frac{ u ^{2^{*}(s)-2}u}{ y ^{s}}+ f(x,u)\) in bounded domain. Replacing the Ambrosetti–Rabinowitz condition by general superquadratic assumptions and the nonquadratic assumption, we establish the existence results of positive solutions. PubDate: 2018-02-09 DOI: 10.1007/s40840-018-0603-3

Authors:Baowei Feng; Khaled Zennir; Lakhdar Kassah Laouar Abstract: An extensible viscoelastic plate equation with a nonlinear time-varying delay feedback and nonlinear source term is considered. Under suitable assumptions on relaxation function, nonlinear internal delay feedback, and source term, we establish a general decay of energy by using the multiplier method if the weight of weak dissipation and the delay satisfy \(\mu _2<\frac{\mu _1\alpha _1(1-d)}{\alpha _2(1-\alpha _1d)}\) , and extend some known results. PubDate: 2018-02-09 DOI: 10.1007/s40840-018-0602-4

Authors:Junfei Cao; Zaitang Huang Abstract: In this paper, we establish a new existence theorem for asymptotically almost periodic mild solutions to a class of semilinear stochastic evolution equations. As one would expect, our result would generalize and improve some related results in this area. PubDate: 2018-02-08 DOI: 10.1007/s40840-018-0604-2

Authors:Yongxin Yuan; Kezheng Zuo; Hao Liu; Wenhua Zhao Abstract: In many areas, there arise linear systems of the form $$\begin{aligned} \left[ \begin{array}{ll} A &{}\quad B^\top \\ B &{}\quad -\,D \\ \end{array} \right] \left[ \begin{array}{c} x \\ y \\ \end{array} \right] =\left[ \begin{array}{c} f \\ g \\ \end{array} \right] , \end{aligned}$$ where \(A \in {\mathbf {R}}^{n\times n}, D \in {\mathbf {R}}^{p\times p}\) are symmetric and positive semi-definite and \(B \in {\mathbf {R}}^{p \times n}.\) In this paper, some simple criteria for this special linear systems to have solutions and the unique solution are provided, and the solvability conditions are expressed by \(A, B, D, f\) and \(g\) . PubDate: 2018-02-06 DOI: 10.1007/s40840-018-0601-5

Authors:Qinghua Hu Abstract: A new characterization for the boundedness, compactness and the essential norm of generalized weighted composition operators from Bloch-type spaces into Zygmund-type spaces are given in this paper. PubDate: 2018-02-05 DOI: 10.1007/s40840-018-0605-1

Authors:Vítor H. Fernandes; Jörg Koppitz; Tiwadee Musunthia Abstract: A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup \(\mathscr {TF}_{n}\) of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of \(\mathscr {TF}_{n}\) and provide a minimal generating set for \( \mathscr {TF}_{n}\) . Moreover, a formula for the number of idempotents in \(\mathscr {TF}_{n}\) is given. PubDate: 2018-01-31 DOI: 10.1007/s40840-017-0598-1

Authors:Kaizhong Guan Abstract: By establishing two new impulsive delay differential inequalities from impulsive perturbation and impulsive control point of view, respectively, constructing some Lyapunov functionals, and employing the matrix measure approach, some novel and sufficient conditions are obtained to guarantee global power stability of neural networks with impulses and proportional delays. The obtained stability criteria are dependent on impulses and the proportional delay factor so that it is convenient to derive some feasible impulsive control laws according to the proportional delay factor allowed by such neural networks. It is shown that impulses can act as stabilizers to globally power stabilize an unstable neural network with proportional delay based on suitable impulsive control laws. Moreover, the power convergence rate can be estimated and obtained by simple computation. Three numerical examples are given to illustrate the effectiveness and advantages of the results obtained. PubDate: 2018-01-16 DOI: 10.1007/s40840-018-0600-6

Authors:Shih-Sen Chang; Ching-Feng Wen; Jen-Chih Yao Abstract: The purpose of this paper is by using a generalized forward–backward splitting method to propose an iterative algorithm for finding a common element of the set of solutions to a system of quasi-variational inclusions with accretive mappings and the set of fixed points for a \(\lambda \) -strictly pseudo-contractive mapping in Banach spaces. Some strong convergence theorems of the sequence generated by the algorithm are proved. The results presented in the paper extend and improve some recent results. As applications, we utilize our results to study the approximation problem of solutions to a system of variational inequalities, accretive variational inequality problem and convex minimization problem in Banach spaces. PubDate: 2018-01-08 DOI: 10.1007/s40840-017-0599-0

Authors:Xinlei Wang; Dein Wong Abstract: In a recent paper, Das introduced the graph \(\mathcal {I}n(\mathbb {V})\) , called subspace inclusion graph on a finite dimensional vector space \(\mathbb {V}\) , where the vertex set is the collection of nontrivial proper subspaces of \(\mathbb {V}\) and two vertices are adjacent if one is properly contained in another. Das studied the diameter, girth, clique number and chromatic number of \(\mathcal {I}n(\mathbb {V})\) when the base field is arbitrary, and he also studied some other properties of \(\mathcal {I}n(\mathbb {V})\) when the base field is finite. At the end of the above paper, the author posed the open problem of determining the automorphisms of \(\mathcal {I}n(\mathbb {V})\) . In this paper, we give the answer to the open problem. PubDate: 2018-01-04 DOI: 10.1007/s40840-017-0597-2

Authors:Reza Aminizadeh; Hamid Rasouli; Abolfazl Tehranian Abstract: In this paper, the notion of (short) quasi-exact sequence of S-acts is introduced. We study the behaviour of quasi-exact sequences in regard to some algebraic properties of S-acts including principal weak injectivity, principal weak flatness, regularity and torsion freeness. Moreover, some results concerning commutative diagrams of modules are generalized to acts over monoids. PubDate: 2018-01-03 DOI: 10.1007/s40840-017-0596-3