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Some new conditions on the entire coefficients A(z) and B(z), which guarantee every nontrivial solution of f''+A(z) f'+B(z) f = 0 is of infinite order, are given in this paper. Two classes of entire functions are involved in these conditions, the one is entire functions having Fabry gaps, the another is function extremal for Yang?s inequality. Moreover, a kind of entire function having finite Borel exception value is considered.

In the present paper, we obtain several sufficient conditions for Carath?odory functions in the open unit disk U = {z ? C : ?z? < 1}. We also obtain sufficient conditions for p-valent or starlike functions. Moreover, we improve some results due to Nunokawa [Tsukuba J. Math. 13 (1989), 453-455] as some special cases of main results.

In the present paper, unique solvability of a source identification inverse problem for a semilinear equation with a final overdetermination in a Banach space is investigated. Moreover, the first order of accuracy Rothe difference scheme is presented for numerically solving this problem. The existence and uniqueness result for this difference scheme is given. The efficiency of the proposed method is evaluated by means of computational experiments.

In this paper, by introducing a parameter ? and ?, using the Euler-Maclaurin expansion for the Riemann zeta function, we establish an inequality of a weight coefficient. Using this inequality, we derive generalizations of a Hilbert?s type inequality.

In this paper, we establish sufficient conditions for the existence and stability of solutions for fractional integro-differential equations with boundary conditions involving complex order. The proofs are based upon the Banach contraction principle. An example is included to show the applicability of our results.

Let $G=(V,\,E)$ be a simple connected graph of order $n$ with $m$ edges. Also let $e_G(v_i)$ be the eccentricity of a vertex $v_i$ in $G$. We can assume that $e_G(v_1)\geq e_G(v_2)\geq \cdots\geq e_G(v_{n-1})\geq e_G(v_n).$ The average eccentricity of a graph $G$ is the mean value of eccentricities of vertices of $G$, $$avec(G)=\frac{1}{n}\,\sum\limits^n_{i=1}\,e_G(v_i)\,.$$ Let $\gamma=\gamma_G$ be the largest positive integer such that $$e_G(v_{\gamma_G})\geq avec(G).$$ In this paper, we study on the value of $\gamma_G$ of a graph $G$. For any tree $T$ of order $n$, we prove that $2\leq \gamma_T\leq n-1$ and characterize the extremal graphs. Moreover, we prove that for any graph $G$ of order $n$, $2\leq \gamma_G\leq n$ and characterize the extremal graphs. Finally some Nordhaus-Gaddum type results are obtained on $\gamma_G$ of general graphs $G$.

In this paper, we give some estimates for the essential norm of weighted composition operators from the Bloch space and the Zygmund space to the Bloch space.

In this paper we introduce f-rough weighted statistical limit set and f-weighted statistical cluster points set which are natural generalizations of rough statistical limit set and f-statistical cluster points set of sequence respectively. Some new examples are constructed to ensure the deviation of basic results. So both the sets don?t follow the nature of usual extension properties which will be discussed here.

In this paper, we first give the modified version of the iteration process of Thakur et al. [15] which is faster than Picard, Mann, Ishikawa, Noor, Agarwal et al. [2] and Abbas et al. [1] processes. Secondly, we prove weak and strong convergence theorems of this iteration process for multivalued quasi nonexpansive mappings in uniformly convex Banach spaces. Thirdly, we support our theorems with analytical examples. Finally, we compare rates of convergence for multivalued version of iteration processes mentioned above via a numerical example.

Let T,S : A U B ? A U B be mappings such that T(A) ? B,T(B)? A and S(A) ? A,S(B)?B. Then the pair (T,S) of mappings defined on A[B is called cyclic-noncyclic pair, where A and B are two nonempty subsets of a metric space (X,d). A coincidence best proximity point p ? A U B for such a pair of mappings (T,S) is a point such that d(Sp,Tp) = dist(A,B). In this paper, we study the existence and convergence of coincidence best proximity points in the setting of convex metric spaces. We also present an application of one of our results to an integral equation.

In this paper, we introduce a notion of the J-kernel of a bounded linear operator on a Krein space and study the J-Fredholm theory for Krein space operators. Using J-Fredholm theory, we discuss when (a-)J-Weyl?s theorem or (a-)J-Browder?s theorem holds for bounded linear operators on a Krein space instead of a Hilbert space.

A strongly direct sum decomposition given by a strongly nil-clean endomorphism motivates us to introduce a class of new Drazin inverses, which is called strong Drazin inverse. In this paper, some basic properties of the strong Drazin inverse are obtained. We show the Cline’s Formula and Jacobson’s Lemma for the strong Drazin inverse. Further, some additive results for the strong Drazin inverse are presented under additional conditions that ab = 0 or ab = ba.

The idea of I-convergence of real sequences was introduced by Kostyrko et al. [Kostyrko, P. ; Sal?t, T. and Wilczy?ski, W. I-convergence, Real Anal. Exchange 26(2) (2000/2001), 669-686] and also independently by Nuray and Ruckle [Nuray, F. and Ruckle,W. H. Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245(2) (2000), 513-527]. In this paper we introduce the concepts of Wijsman I-lacunary statistical convergence of order ? and Wijsman strongly I-lacunary statistical convergence of order ?, and investigated between their relationship.

In this paper, the concepts of C-precontinuous posets, quasi C-precontinuous posets and meet Cprecontinuous posets are introduced. The main results are: (1) A complete semilattice P is C-precontinuous (resp., quasi C-precontinuous) if and only if its normal completion is a C-continuous lattice (resp., quasi C-continuous lattice); (2) A poset is both quasi C-precontinuous and Frink quasicontinuous if and only if it is generalized completely continuous; (3) A complete semilattice is meet C-precontinuous if and only if its normal completion is meet C-continuous; (4) A poset is both quasi C-precontinuous and meet C-precontinuous if and only if it is C-precontinuous.

In this paper, firstwe give some necessary and sufficient conditions for multiplication conditional type operators between two Lp-spaces to have closed range. Then we investigate Fredholm ones when the underlying measure space is non-atomic. Finally we give some examples.

The main purpose of this paper is to derive some inequality properties, convolution properties, subordination and superordination properties, and sandwich-type results of a certain family of multiplier transforms.

In this paper, we generalized a known theorem dealing with absolute weighted arithmetic mean summability of infinite series by using a quasi-f-power increasing sequence instead of a quasi-?-power increasing sequence. And we applied it to the trigonometric Fourier series

In this paper, we mainly consider Schwarz lemma for holomorphic functions and contraction properties of holomorphic functions with respect to Kobayashi distances. We also review some results related to the subject using some novelty and announce a few new results.

Beer and Di Concilio [4] have given necessary and sufficient conditions for a two-sided Attouch-Wets topology to contain another on the hyperspace of non-empty closed subsets of a metrizable space as determined by metrics compatible with the topology. In the present paper, we characterize comparability of lower Attouch-Wets topologies as determined by compatible metrics.

In this paper, Cline's formula for the well-known generalized inverses such as Drazin inverse, pseudo Drazin inverse and generalized Drazin inverse is extended to the case when $\left\{ \begin{aligned} acd=dbd \ \\ dba=aca. \\ \end{aligned} \right.$ Also, applications are given to some interesting Banach space operator properties like algebraic, meromorphic, polaroidness and B-Fredholmness.

In this paper, we introduce the concept of a modified F-contraction via ?-admissible mappings and propose some theorems that guarantee the existence and uniqueness of fixed point for such mappings in the frame of complete metric spaces. We also provide some illustrative examples. Moreover, we consider an application solving an integral equation.

In this paper we study the existence of positive solutions for the fractional $p$-Laplacian boundary value problem \[\left\{\aligned & D_{0+}^\beta (\phi_p (D_{0+}^\alpha u(t)))=f(t,u(t)), t\in (0,1),\\ & u(0)=u'(0)=0, u'(1)=au'(\xi), D_{0+}^\alpha u(0)=0, D_{0+}^\alpha u(1)= b D_{0+}^\alpha u(\eta), \endaligned \right.\] where $2 1$, $\phi_p^{-1}=\phi_q$, $1/p+1/q=1$, $0

In the present paper, it is studied the boundary behavior of the so-called lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions on the function Q(z) for a homeomorphic extension of the given mappings to the boundary by prime ends. The developed theory is applied to mappings with finite distortion by Iwaniec, also to solutions of the Beltrami equations, as well as to finitely bi-Lipschitz mappings that a far-reaching extension of the known classes of isometric and quasiisometric mappings.

In this work, our intention is to introduce the notion of rational (?-?-FG)-contraction mapping in b-metric-like spaces, and produce relevant fixed point and periodic point results for weakly ?-admissible mappings. Ulam-Hyers stability of this problem is also investigated. To illustrate our results, we give throughout the paper some examples, in particular in order to justify the use of rational terms. As an application, we obtain sufficient conditions for the existence of solutions for Cantilever Beam Problem.

In this paper, we study the growth of gradients of solutions of elliptic equations, including the Dirichlet eigenfunction solutions on bounded plane convex domain. Several results related to Bi-Lipschicity of quasiconformal harmonic (qch) mappings with respect to quasi-hyperbolic and euclidean metrics, are proved. In connection with the subject, we announce a few results concerning the so called interior estimate, including Proposition 1.1. In addition, a short review of the subject is given.

In this paper, we discuss few existence result for solution of an infinite system of fractional differential equations of order ?(1 < ? < 2), with three point boundary value problem in the interval [0, T]. The problem is studied in the classical Banach sequence spaces c0 and lp (1 ? p < 1), using Hausdorff measure of noncompactness and Darbo type fixed point theorem. We also illustrate our results through some concrete examples.

In this paper, we study Weyl type theorems for complex symmetric operator matrices. In particular, we give a necessary and sufficient condition for complex symmetric operator matrices to satisfy a-Weyl?s theorem. Moreover, we also provide the conditions for such operator matrices to satisfy generalized a-Weyl?s theorem and generalized a-Browder?s theorem, respectively. As some applications, we give various examples of such operator matrices which satisfy Weyl type theorems.

In this paper we introduce and study some properties of k-bi-starlike functions defined by making use of the S?l?gean derivative operator. Upper bounds on the second Hankel determinant for k-bi-starlike functions are investigated. Relevant connections of the results presented here with various well-known results are briefly indicated.

The purpose of this paper is to introduce the notion $\mathcal{I}$-$\left[V,\lambda \right]$-summability and $\mathcal{I_\lambda}- $statistical convergence of order $\alpha$ with respect to the intuitionistic fuzzy norm $\left( \mu ,v\right) $, investigate their relationship, and make some observations about these classes. We mainly study the relation between these two new methods as also the relation between $\mathcal{I_\lambda}$-statistical convergence of order $\alpha$ and $\mathcal{I}$-statistical convergence of order $\alpha$ in intuitionistic fuzzy normed space $\left( \mu ,v\right) $.

In this paper, several results involving the derived WP-Bailey pairs of sequences are established. Furthermore, by using these results, a number of transformation formulas for basic (or q-) hypergeometric series are derived.

The aim of this paper is to construct a new braided T-category via the generalized Yetter-Drinfel?d modules and Drinfel?d codouble over a Hopf algebra, an approach different from that proposed by Panaite and Staic [1]. Moreover, in the case of finite dimensional, we will show that this category coincides with the corepresentation of a certain coquasitriangular Turaev group algebra which we construct. Finally we apply our theory to the case of group algebra.

In this paper, we shall establish some Fej?r-type inequalities for L-Lipschitzian functions. These inequalities can connect with Fej?r inequality (1). Also, some applications to convex function, ?-th moment, mathematical expectation of a random variable and Euler?s Beta function are provided.

One impetus for writing this paper is the issue of approximation pseudospectrum introduced by M. P. H.Wolff in the journal of approximation theory (2001). The latter study motivates us to investigate the essential approximation pseudospectrum of closed, densely defined linear operators on a Banach space. We begin by defining it and then we focus on the characterization, the stability and some properties of these pseudospectra.

In this paper, we investigate the existence of minimal nonnegative solution for a class of nonlinear fractional integro-differential equations on semi-infinite intervals in Banach spaces by applying the cone theory and the monotone iterative technique. An example is given for the illustration of main results.

In this paper, we develop the existence criteria for the solutions of a system of Hadamard type sequential fractional differential equations with variable coefficients and nonlocal integral boundary conditions. The main results rely on the standard tools of fixed-point theory. An illustrative example is also discussed.

In this paper we introduce a new algorithm based on the viscosity iteration method for solving the split common fixed point problem of two infinite families of k-demicontractive mappings. We shall also study the split common null point problem, and the split equilibrium problem for this class of mappings. As an application, we obtain strong convergence theorems for the split monotone variational inclusion problem and the split variational inequality problem. Our results improve and extend the recent results of Cui and Wang [9], Takahashi [21], Tang and Lui [22], Moudafi [15], Eslamian and Vahidi [17], and many others.

In this paper, we prove Sherman like inequalities for convex sequences and nondecreasing convex functions. Thus we develop some results by S. Wu and L. Debnath [19]. In consequence, we derive discrete versions for convex sequences of Petrovic and Giaccardi?s inequalities. As applications, we establish some generalizatons of Fej?r inequality for convex sequences. We also study inequalities of Hermite-Hadamard type. Thus we extend some recent results of Latreuch and Bela?di [8]. In our considerations we use some matrix methods based on column stochastic and doubly stochastic matrices.

For a simple graph G, the Q-eigenvalues are the eigenvalues of the signless Laplacian matrix Q of G. A Q-eigenvalue is said to be a Q-main eigenvalue if it admits a corresponding eigenvector non orthogonal to the all-one vector, or alternatively if the sum of its component entries is non-zero. In the literature the trees, unicyclic, bicyclic and tricyclic graphs with exactly two Q-main eigenvalues have been recently identied. In this paper we continue these investigations by identifying the trees with exactly three Q-main eigenvalues, where one of them is zero.

The object of the present paper is to study Ricci semisymmetric contact metric manifolds. As a consequence of the main result we deduce some important corollaries. Besides these we study contact metric manifolds satisfying the curvature condition Q,R = 0, where Q and R denote the Ricci operator and curvature tensor respectively. Also we study the symmetric properties of a second order parallel tensor in contact metric manifolds. Finally, we give an example to verify the main result.

In this paper we have extended the concepts of I-limit superior and I-limit inferior to I-statistical limit superior and I-statistical limit inferior and studied some of their properties for sequence of real numbers.

In a recent article, Khojasteh et al. introduced a new class of simulation functions, Z-contractions, with blending over known contractive conditions in the literature. Subsequently, in this paper, we extend and generalize the results in ?-metric context and we discuss some fixed point results in connection with existing ones. Also, we originate the notion of modified Z-contractions and explore the existence and uniqueness of fixed points of such functions on the said spaces. Finally we include examples to instantiate our main results.

Let $R$ be a commutative ring with identity and $X$ be a Tychonoff space. An ideal $I$ of $R$ is Von Neumann regular (briefly, regular) if for every $a\in I$, there exists $b\in R$ such that $a=a^2b$. In the present paper, we obtain the general form of a regular ideal in $C(X)$ which is $O^A$, for some closed subset $A$ of ${\beta X}$, for which $ A^c\cap X\subseteq (P(X))^{\circ }$, where $P(X)$ is the set of all $P$-points of $X$. We show that the ideals and subrings such as $C_K(X)$, $C_\psi(X)$, $C_\infty(X)$, $Soc_mC(X)$ and $M^{\beta X\backslash X}$ are regular if and only if they are equal to the socle of $C(X)$. We carry further the study of maximal regular ideal, for instance, it is shown that for a vast class of topological spaces (we call them $OPD$-spaces) the maximal regular ideal is $O^{X\backslash I(X)}$, where $I(X)$ is the set of nonisolated points of $X$. Also, for this class, the socle of $C(X)$ is the maximal regular ideal if and only if $I(X)$ contains no infinite closed set. We also show that $C(X)$ contains an ideal which is both essential and regular if and only if $(P(X))^{\circ }$ is dense in $X$. Finally it is shown that, for semiprimitive rings pure ideals are of the form $O^A$ which $A$ is a closed subset of $Max(R)$, also a $P$-point of $X=Max(R)$ is introduced and it is shown that the maximal regular ideal of an arbitrary ring $R$ is $O^{X\backslash P(X)}$, which $P(X)$ is the set of $P$-points of $X=Max(R)$

In this paper, we study the generalization Bernoulli numbers and polynomials attached to a periodic group homomorphism from a finite cyclic group to the set of complex numbers and derive new periodic group homomorphism by using a fixed periodic group homomorphism. Hence, we obtain not only multiplication formulas, but also some new identities for the generalized Bernoulli polynomials attached to a periodic group homomorphism.

In this paper, we give some formulas for the Drazin inverses of the sum of two matrices under conditions weaker than those used in some current literature. Also, we obtain representation for the Drazin inverse of a complex block matrix under some conditions.

Let (X; d) be a metric space, Y ? X a nonempty closed subset of X and let f : Y ? X be a non self operator. In this paper we study the following problem: under which conditions on f we have all of the following assertions: 1. The operator f has a unique fixed point; 2. The operator f satisfies a retraction-displacement condition; 3. The fixed point problem for f is well posed; 4. The operator f has the Ostrowski property. Some applications and open problems related to these questions are also presented.

This paper is concerned with a more general model of multi-group models with multiple dispersal and stochastic perturbation, in which dispersal among multiple groups and stochastic perturbation are considered at the same time. By combining graph theory with Lyapunov method, we derive two types of sufficient criteria which are in the form of Lyapunov-type and coefficient-type respectively, to guarantee the global exponential stability of the model. Furthermore, coefficient-type criterion is successfully applied to stochastic coupled oscillators system. Finally, we offer a numerical example to illustrate the effectiveness and feasibility of the main results.

In this paper, we obtain some characterizations of centered and binormal operators via Moore-Penrose inverse and Aluthge transform.

In this paper, we construct generalized Baskakov Kantorovich operators. We establish some direct results and then study weighted approximation, simultaneous approximation and statistical convergence properties for these operators. Finally, we obtain the rate of convergence for functions having a derivative coinciding almost everywhere with a function of bounded variation for these operators.

In this paper, we introduce the notion of Saphar linear relation in a Banach space and we study the behaviour of such notion in polynomials.

The q-digamma function ?q(x) and the q-polygamma functions ?(r)q(x), r ? N = {1,2,...} are defined for all x > 0 and 0 < q < 1. In this paper, the neutrices and the neutrix limit are used to define the q-digamma function q(x) and the q-polygamma functions ?(r)q(x), r ? N for all x ? R. Moreover, further results are given.