Authors:M. Mursaleen; Khursheed J. Ansari Pages: 1479 - 1491 Abstract: In this paper, we study some approximation properties of q-analogue of Stancu-Beta operators which preserve \(x^{2}\) . We determine the rate of global convergence in weighted spaces. We also prove the Voronovskaja-type theorem for these operators. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0146-9 Issue No:Vol. 40, No. 4 (2017)

Authors:Ana M. Cabrera-Serrano; Juan F. Mena-Jurado Pages: 1613 - 1621 Abstract: G-spaces are a class of \(L_1\) -preduals introduced by Grothendieck. We prove that if every extreme operator from any Banach space into a G-space, X, is a nice operator (that is, its adjoint preserves extreme points), then X is isometrically isomorphic to \(c_0(I)\) for some set I. One of the main points in the proof is a characterization of spaces of type \(c_0(I)\) by means of the structure topology on the extreme points of the dual space. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0155-8 Issue No:Vol. 40, No. 4 (2017)

Authors:Mamoru Nunokawa; Janusz Sokół; Nak Eun Cho Pages: 1791 - 1800 Abstract: The purpose of the present paper is to prove a geometric property for analytic functions p in the open unit disk with \(p(0)=1\) by using Nunokawa’s result, which is a generalized form of well-known Jack’s lemma. This property concerns a boundary behavior of the functions p. As the applications of the main result, we obtain a few corollaries where several sufficient conditions for p to be of the real part greater than a given number \(\beta \ (0\le \beta <1)\) are also investigated. PubDate: 2017-10-01 DOI: 10.1007/s40840-016-0398-z Issue No:Vol. 40, No. 4 (2017)

Authors:Guanggang Liu; Shaoyun Shi; Yucheng Wei Abstract: In this paper we consider a class of Kirchhoff-type problem with 2-superlinear potentials. The existence of one positive solution and one negative solution will be established by using iterative technique and the Mountain Pass theorem, and a sign changing solution will be obtained by combining iterative technique and the Nehari method. PubDate: 2017-11-13 DOI: 10.1007/s40840-017-0571-z

Authors:Zhen Lin; Shu-Guang Guo; Ke Luo Abstract: The Laplacian spread of a graph G is defined to be the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of G. Let \({\mathcal {Q}}_t(n, d)=\{G\, \, G-v_0\ \hbox {is a tree on }n-1\hbox { vertices and } d_G(v_0)=d\}.\) Recently, Y. Xu and J. Meng characterized the unique graph with maximum Laplacian spread among all graphs in the set \({\mathcal {Q}}_t(n, d)\) with \(1\le d\le (n-4)/2\) . In this paper, we extend their result by determining the unique graph with maximum Laplacian spread among all graphs in the set \({\mathcal {Q}}_t(n, d)\) with \(1\le d\le n-5\) . PubDate: 2017-11-11 DOI: 10.1007/s40840-017-0572-y

Authors:Ricardo Almeida Abstract: In this paper, we discuss the existence and uniqueness of solutions of a boundary value problem for a fractional differential equation of order \(\alpha \in (2,3)\) , involving a general form of fractional derivative. First, we prove an equivalence between the Cauchy problem and the Volterra equation. Then, two results on the existence of solutions are proven, and we end with some illustrative examples. PubDate: 2017-11-11 DOI: 10.1007/s40840-017-0569-6

Authors:Gui-Xian Tian; Jing-Xiang He; Shu-Yu Cui Abstract: Many variants of join operations of graphs have been introduced, and their spectral properties have been studied extensively by many researchers. This paper mainly focuses on the Laplacian spectra of some double join operations of graphs. We first introduce the conception of double join matrix and provide a complete information about its eigenvalues and the corresponding eigenvectors. Further, we define four variants of double join operations based on subdivision graph, Q-graph, R-graph and total graph. Applying the result obtained about double join matrices, we give an explicit complete characterization of the Laplacian eigenvalues and the corresponding eigenvectors of four variants in terms of the Laplacian eigenvalues and the eigenvectors of factor graphs. These results generalize some well-known results on the Laplacian spectra of some join operations of graphs. PubDate: 2017-11-11 DOI: 10.1007/s40840-017-0566-9

Authors:Zbigniew Leśniak Abstract: We study the problem of topological conjugacy of Brouwer flows. We give a sufficient and necessary condition for Brouwer flows to be topologically conjugate. To obtain this result we use a cover of the plane by maximal parallelizable regions and relations between parallelizing homeomorphisms of these regions. We show that for topologically equivalent Brouwer flows there exists a one-to-one correspondence between such covers of the plane. PubDate: 2017-11-11 DOI: 10.1007/s40840-017-0567-8

Authors:Yaser Alizadeh; Tomislav Došlić; Kexiang Xu Abstract: Let G be a simple connected graph. The eccentric complexity of graph G is introduced as the number of different eccentricities of its vertices. A graph with eccentric complexity equal to one is called self-centered. In this paper, we study the eccentric complexity of graph under several graph operations such as complement of graph, line graph, Cartesian product, sum, disjunction and symmetric difference of graphs. Also, we present an infinite family of non-vertex-transitive self-centered graphs and we prove that all such graphs are 2-connected. Further, for any D and k where \(k \le \frac{D-1}{2}\) , we construct an infinite family of non-vertex-transitive graphs with eccentric complexity k and diameter D. Extremal graphs with minimum or maximum total eccentricity among all graphs with given eccentric complexity are determined. We also consider a family of nanotubes and show that it is extremal with respect to the eccentric complexity among all fullerene graphs. At the end we also indicate some possible directions of further research. PubDate: 2017-11-09 DOI: 10.1007/s40840-017-0564-y

Authors:René Erlin Castillo; Humberto Rafeiro; Julio C. Ramos-Fernández; Margot Salas-Brown Abstract: We calculate the measure of non-compactness of the multiplication operator \(M_u\) acting on non-atomic Köthe spaces. We show that all bounded below multiplication operators acting on Köthe spaces are surjective and therefore bijective and we give some new characterizations about closedness of the range of \(M_u\) acting on Köthe spaces. PubDate: 2017-11-09 DOI: 10.1007/s40840-017-0562-0

Authors:Minjia Shi; Rongsheng Wu; Liqin Qian; Lin Sok; Patrick Solé Abstract: In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring \(R=\mathbb {F}_p+u\mathbb {F}_p+\cdots +u^{k-1}\mathbb {F}_{p},\) with \(u^k=0,\) are constructed that generalize the construction of Shi et al. (IEEE Commun. Lett. 20(12):2346–2349, 2016), which is the special case of \(p=k=2.\) These codes are defined as trace codes. In some cases of their defining sets, they are abelian. Their homogeneous weight distributions are computed by using exponential sums. In particular, in the two-weight case, we give some conditions of optimality of their Gray images by using the Griesmer bound. Their dual homogeneous distance is also given. The codewords of these codes are shown to be minimal for inclusion of supports, a fact favorable to an application to secret sharing schemes. PubDate: 2017-10-28 DOI: 10.1007/s40840-017-0553-1

Authors:Nihal Yilmaz Özgür; Nihal Taş Abstract: The fixed-point theory and its applications to various areas of science are well known. In this paper, we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We verify our results by illustrative examples. PubDate: 2017-10-28 DOI: 10.1007/s40840-017-0555-z

Authors:Farzad Ismail; Wei Shyang Chang; Hossain Chizari Abstract: In this paper, the properties of the newly developed flux-difference residual distribution methods will be analyzed. The focus would be on the order-of-accuracy and stability variations with respect to changes in grid skewness. Overall, the accuracy loss and the stability range of the new methods are comparable with the existing residual distribution methods. It will also be shown that new method has a general mathematical formulation which can easily recover the existing residual distribution methods. PubDate: 2017-10-26 DOI: 10.1007/s40840-017-0559-8

Authors:Jing Ren; Chengbo Zhai Abstract: In this paper, by applying the cone theory in ordered Banach spaces associated with the characters of increasing \(\varphi -(h,e)\) -concave operators, we investigate the existence and uniqueness of nontrivial solutions for a nonlinear fractional q-difference equation boundary value problem. The main results show that we can construct an iterative scheme approximating the unique nontrivial solution. Relying on an example, we show the efficiency and applicability of the main result. PubDate: 2017-10-26 DOI: 10.1007/s40840-017-0560-2

Authors:Nikiforos Mimikos-Stamatopoulos; Nikolaos S. Papageorgiou Abstract: We consider a semilinear Robin problem with indefinite and unbounded potential and a reaction term which asymptotically at \(\pm \,\infty \) is resonant with respect to any nonprincipal, nonnegative eigenvalue of the differential operator. Using critical point theory, Morse theory (critical groups) and the reduction method, we show that the problem has at least three nontrivial solutions. PubDate: 2017-10-26 DOI: 10.1007/s40840-017-0561-1

Authors:Subzar Beig; V. Ravichandran Abstract: The convolution properties are discussed for the complex-valued harmonic functions on the unit disk \(\mathbb {D}\) constructed from the harmonic shearing of the analytic function \(\phi (z):=\int _0^z (1-2\xi \textit{e}^{\textit{i}\mu }\cos \nu +\xi ^2\textit{e}^{2\textit{i}\mu })^{-1}{} \textit{d}\xi \) , where \(\mu \) and \(\nu \) are real numbers. For any real number \(\alpha \) and a harmonic function \(f=h+\overline{g}\) , define an analytic function \(f_{\alpha }\) by \(f_{\alpha }:=h+\textit{e}^{-2\textit{i}\alpha }g\) . Let \(\mu _1\) and \(\mu _2\) \((\mu _1+\mu _2=\mu )\) be real numbers, and \(f=h+\overline{g}\) and \(F=H+\overline{G}\) be locally univalent and sense-preserving harmonic functions such that \(f_{\mu _1}*F_{\mu _2}=\phi \) . It is shown that the convolution \(f*F\) is univalent and convex in the direction of \(-\,\mu \) , provided it is locally univalent and sense-preserving. Also, local univalence of the above convolution \(f*F\) is shown when f and F have specific analytic dilatations. Furthermore, if \(g\equiv 0\) and both the analytic functions \(f_{\mu _1}\) and \(F_{\mu _2}\) are convex, then the convolution \(f*F\) is shown to be convex. These results extend the work of Dorff et al. (Complex Var Elliptic Equ 57(5):489–503, 2012) to a larger class of functions. PubDate: 2017-10-22 DOI: 10.1007/s40840-017-0552-2

Authors:Mohamed M. S. Nasser Abstract: This paper presents a numerical method for computing the conformal mappings onto the parabolic slit domain, the elliptic slit domain and the hyperbolic slit domain. The method relies on a boundary integral equation with the generalized Neumann kernel. For a given multiply connected domain of connectivity \(m+1\) , the proposed method requires \(O((m+1)n\log n)\) operations where n is the number of nodes in the discretization of each boundary component of the given domain. Several numerical examples are presented to illustrate the performance of the proposed method. PubDate: 2017-10-22 DOI: 10.1007/s40840-017-0558-9

Authors:Daniel de la Fuente; Francisco J. Palomo; Alfonso Romero Abstract: In this paper, we develop a formula for spacelike surfaces in a four-dimensional Lorentzian space form which involves its mean curvature vector field, the Gauss curvature of the induced metric and the Gauss curvature of the second fundamental form associated to a non-degenerate null normal section. By means of this formula, we establish several sufficient conditions for a compact spacelike surface in a four-dimensional Lorentzian space form which has a null umbilical normal direction. As another application, we give a new proof of Liebmann rigidity theorems in Euclidean, hemispherical, hyperbolic spaces and in the De Sitter spacetime. PubDate: 2017-10-20 DOI: 10.1007/s40840-017-0557-x

Authors:Li Du; Juan Zhang Abstract: In this paper, we investigate biharmonic submanifolds with parallel normalized mean curvature vector field in pseudo-Riemannian space forms and classify completely such pseudo-umbilical submanifolds. Also, we prove that such submanifolds have parallel mean curvature vector field under the assumption that they have diagonalizable shape operator with at most two distinct principal curvatures in the direction of the mean curvature vector field, and apply it to obtain a partial classification result. PubDate: 2017-10-17 DOI: 10.1007/s40840-017-0556-y

Authors:Liwei Wang; Lisheng Shu Abstract: In this paper, we study the boundedness of multilinear commutators of Hardy–Littlewood maximal operators in variable exponent Herz and Herz–Morrey spaces, which in turn are used to obtain the boundedness for a large class of the multilinear commutators related to sublinear operators. Moreover, based on the atomic decomposition and on generalization of the BMO norm, we study the boundedness of multilinear commutators of singular integral operators with Calderón–Zygmund kernels in variable exponent Herz-type Hardy spaces. PubDate: 2017-10-09 DOI: 10.1007/s40840-017-0554-0