Authors:Nguyen Van Thin Pages: 1413 - 1442 Abstract: 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: 2017-10-01 DOI: 10.1007/s40840-017-0492-x Issue No:Vol. 40, No. 4 (2017)

Authors:H. Abdollahzadeh Ahangar; Teresa W. Haynes; J. C. Valenzuela-Tripodoro Pages: 1443 - 1454 Abstract: Abstract Let \(G = (V, E)\) be a simple graph with vertex set V and edge set E. A mixed Roman dominating function (MRDF) of G is a function \(f: V\cup E\rightarrow \{0,1,2\}\) satisfying the condition every element \(x\in V\cup E\) for which \(f(x)= 0\) is adjacent or incident to at least one element \(y\in V\cup E\) for which \(f(y) = 2\) . The weight of a MRDF f is \(\omega (f)=\sum _{x\in V\cup E}f(x)\) . The mixed Roman domination number of G is the minimum weight of a mixed Roman dominating function of G. In this paper, we initiate the study of the mixed Roman domination number and we present bounds for this parameter. We characterize the graphs attaining an upper bound and the graphs having small mixed Roman domination numbers. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0141-1 Issue No:Vol. 40, No. 4 (2017)

Authors:Dijana Mosić Pages: 1465 - 1478 Abstract: Abstract Under new conditions on Banach algebra elements a and b, we derive explicit expressions for the generalized Drazin inverse of the sum \(a+b\) . As an application of our results, we present new representations for the generalized Drazin inverse of a block matrix in a Banach algebra. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0143-z Issue No:Vol. 40, No. 4 (2017)

Authors:M. Mursaleen; Khursheed J. Ansari Pages: 1479 - 1491 Abstract: 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:Haihua Qin; Jingmei Lu Pages: 1493 - 1522 Abstract: Abstract In this paper, a Cauchy problem for the Helmholtz equation is investigated. It is well known that this problem is severely ill-posed in the sense that the solution (if it exists) does not depend continuously on the given Cauchy data. To overcome such difficulties, we propose a modified regularization method to approximate the solution of this problem, and then analyze the stability and convergence of the proposed regularization method based on the conditional stability estimates. Finally, we present two numerical examples to illustrate that the proposed regularization method works well. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0148-7 Issue No:Vol. 40, No. 4 (2017)

Authors:Jianwen Zhou; Yongkun Li; Yanning Wang Pages: 1523 - 1543 Abstract: Abstract In this paper, we present a recent approach via variational methods and critical point theory to obtain the existence of periodic solutions for a class of delay Hamiltonian systems on time scales with impulsive effects. The variational principle is given, and some existence theorems and two multiplicity results of periodic solutions are obtained. Finally, one example is presented to illustrate the feasibility and effectiveness of our results. Our results are new even in both the differential equations case and the difference equations case. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0149-6 Issue No:Vol. 40, No. 4 (2017)

Authors:Noômen Jarboui; Manar El Islam Toumi Pages: 1545 - 1557 Abstract: Abstract The main purpose of this paper is to study maximal non-Mori subrings R of a domain S. We give characterizations of such domains in several cases. If the ring R is semilocal, (R, S) is a normal pair, and R is a maximal non-Mori subring of S, we give sharp upper bounds for the number of rings and the length of chains of rings in [R, S], the set of intermediate rings. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0150-0 Issue No:Vol. 40, No. 4 (2017)

Authors:Fortuné Massamba Pages: 1559 - 1575 Abstract: Abstract In this paper, our main remark is that proper totally contact umbilical integral manifolds of screen integrable null hypersurfaces in indefinite Kenmotsu manifolds admit \(\eta \) -Weyl structures. Its geometry is closely related to the one of a normal subbundle over the indefinite Kenmotsu manifold. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0152-y Issue No:Vol. 40, No. 4 (2017)

Authors:Ghasem A. Afrouzi; Vicenţiu D. Rădulescu; Saeid Shokooh Pages: 1591 - 1611 Abstract: Abstract In the present paper, we establish the range of two parameters for which a non-homogeneous boundary value problem admits at least three weak solutions. The proof of the main results relies on recent variational principles due to Ricceri. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0153-x Issue No:Vol. 40, No. 4 (2017)

Authors:Ana M. Cabrera-Serrano; Juan F. Mena-Jurado Pages: 1613 - 1621 Abstract: 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:Luis M. Fernández; A. Prieto-Martín Pages: 1623 - 1637 Abstract: Abstract We introduce para-S-manifolds and obtain some results concerning the curvature of these manifolds. In particular, we prove that there does not exist Einstein para-S-manifold, and consequently, we investigate \(\eta \) -Einstein para-S-manifolds and the conditions for them to be \(\xi \) -conformally flat. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0156-7 Issue No:Vol. 40, No. 4 (2017)

Authors:M. Mastyło; E. A. Sánchez Pérez Pages: 1653 - 1675 Abstract: Abstract We study factorization of operators between quasi-Banach spaces. We prove the equivalence between certain vector norm inequalities and the factorization of operators through Orlicz spaces. As a consequence, we obtain the Maurey–Rosenthal factorization of operators into \(L_p\) -spaces. We give several applications. In particular, we prove a variant of Maurey’s Extension Theorem. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0158-5 Issue No:Vol. 40, No. 4 (2017)

Authors:Suhail Gulzar; N. A. Rather Pages: 1691 - 1700 Abstract: Abstract In this paper, certain refinements and generalizations of some inequalities concerning the polynomials and their polar derivative are obtained. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0183-4 Issue No:Vol. 40, No. 4 (2017)

Authors:Rong Hu; Ya Ping Fang Pages: 1733 - 1744 Abstract: Abstract The aim of this paper is to study the well-posedness of the split inverse variational inequality problem. We extend the notion of well-posedness to the split inverse variational inequality problem and establish Furi–Vignoli-type characterizations for the well-posedness. We prove that the well-posedness of the split inverse variational inequality problem is equivalent to the existence and uniqueness of its solution. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0213-2 Issue No:Vol. 40, No. 4 (2017)

Authors:María G. Corrales García; Dolores Martín Barquero; Cándido Martín González; Mercedes Siles Molina; José F. Solanilla Hernández Pages: 1745 - 1767 Abstract: Abstract This paper is devoted to the study of the center of several types of path algebras associated to a graph E over a field K. First we consider the path algebra KE and prove that if the number of vertices is infinite then the center is zero; otherwise, it is K, except when the graph E is a cycle in which case the center is K[x], the polynomial algebra in one indeterminate. Then we compute the centers of prime Cohn and Leavitt path algebras. A lower and an upper bound for the center of a Leavitt path algebra are given by introducing the graded Baer radical for graded algebras. In the final section we describe the center of a prime graph C \(^*\) -algebra for a row-finite graph. PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0214-1 Issue No:Vol. 40, No. 4 (2017)

Authors:Ran Gu; Xueliang Li; Zhongmei Qin; Yan Zhao Pages: 1769 - 1779 Abstract: Abstract An edge-coloring of a connected graph is a monochromatically-connecting coloring (MC-coloring, for short) if there is a monochromatic path joining any two vertices, which was introduced by Caro and Yuster. Let mc(G) denote the maximum number of colors used in an MC-coloring of a graph G. Note that an MC-coloring does not exist if G is not connected, in which case we simply let \(mc(G)=0\) . In this paper, we characterize all connected graphs of size m with \(mc(G)=1, 2, 3, 4\) , \(m-1\) , \(m-2\) and \(m-3\) , respectively. We use G(n, p) to denote the Erdős-Rényi random graph model, in which each of the \(\left( {\begin{array}{c}n\\ 2\end{array}}\right) \) pairs of vertices appears as an edge with probability p independent from other pairs. For any function f(n) satisfying \(1\le f(n)<\frac{1}{2}n(n-1)\) , we show that if \(\ell n \log n\le f(n)<\frac{1}{2}n(n-1)\) , where \(\ell \in \mathbb {R}^+\) , then \(p=\frac{f(n)+n\log \log n}{n^2}\) is a sharp threshold function for the property \(mc\left( G\left( n,p\right) \right) \ge f(n)\) ; if \(f(n)=o(n\log n)\) , then \(p=\frac{\log n}{n}\) is a sharp threshold function for the property \(mc\left( G\left( n,p\right) \right) \ge f(n)\) . PubDate: 2017-10-01 DOI: 10.1007/s40840-015-0274-2 Issue No:Vol. 40, No. 4 (2017)

Authors:D. K. Thomas; S. Abdul Halim Pages: 1781 - 1790 Abstract: Abstract Let f be analytic in \(D=\{z: z < 1\}\) with \(f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}\) . Suppose that \(S^*\) is the class of starlike functions, and K is the class of close-to-convex functions. The paper instigates a study of finding estimates for Toeplitz determinants whose elements are the coefficients \(a_{n}\) for f in \(S^*\) and K. PubDate: 2017-10-01 DOI: 10.1007/s40840-016-0385-4 Issue No:Vol. 40, No. 4 (2017)

Authors:Mamoru Nunokawa; Janusz Sokół; Nak Eun Cho Pages: 1791 - 1800 Abstract: 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:Andrew Rajah; Lois Adewoye Ademola Pages: 1817 - 1828 Abstract: Abstract It is known that all Moufang loops of order \(p^4\) are associative if p is a prime greater than 3. Also, nonassociative Moufang loops of order \(p^5\) (for all primes p) and \(pq^3\) (for distinct odd primes p and q, with the necessary and sufficient condition \(q\equiv 1({\text{ mod }}\ p)\) ) have been proved to exist. Consider a Moufang loop L of order \(p^{\alpha }q^{\beta }\) where p and q are odd primes with \(p<q\) , \(q\not \equiv 1 ({\text{ mod }}\ p)\) and \(\alpha ,\beta \in {\mathbb {Z}}^+\) . It has been proved that L is associative if \(\alpha \le 3\) and \(\beta \le 3\) . In this paper, we extend this result to the case \(p>3\) , \(\alpha \le 4\) and \(\beta \le 3\) . PubDate: 2017-10-01 DOI: 10.1007/s40840-017-0471-2 Issue No:Vol. 40, No. 4 (2017)

Authors:Liwei Wang; Lisheng Shu Abstract: 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