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In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

In the present paper, we prove the convolutions of generalized harmonic right half-plane mappings with harmonic vertical strip mappings are univalent and convex in the horizontal direction. Furthermore, we use a simple method to prove the Theorem~\ref{thmD} that has been proved Kumar~\cite[Theorem 2.4]{Kumar2}. Finally, some examples of harmonic univalent mappings convex in the horizontal direction are also constructed to illuminate our main results.

In this paper, we consider the problem of planarity and outerplanarity of iterated line graphs of the unit, unitary and total graphs when R is a finite commutative ring. We give a full characterization of all these graphs with respect to their planarity and outerplanarity indexes.

The main aim of this paper is to obtain a improved and generalized version of companion of Ostrowski type integral inequalities for mappings whose first derivatives are of bounded variation. Some previous results are also recaptured as special cases. New quadrature formulae are also provided.

In this paper, we study warped product bi-slant submanifolds of cosymplectic manifolds. It is shown that there is no proper warped product bi-slant submanifold other than pseudo-slant warped product. Finally, we give an example of warped product pseudo-slant submanifolds.

The development of a new five-stages symmetric two-step method of fourteenth algebraic order with vanished phase-lag and its first, second, third and fourth derivatives is analyzed in this paper. More specifically: (1) we will present the development of the new method, (2) we will determine the local truncation error (LTE) of the new proposed method, (3) we will analyze the local truncation error based on the radial time independent Schr?dinger equation, (4) we will study the stability and the interval of periodicity of the new proposed method based on a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, (5) we will test the efficiency of the new obtained method based on its application on the coupled differential equations arising from the Schr?dinger equation.

In this paper, we investigate Ricci pseudo-symmetric and Ricci generalized pseudo-symmetric P-Sasakian manifolds. Next we study P-Sasakian manifolds satisfying the curvature condition S ? R = 0. Finally, we give an example of a 5-dimensional P-Sasakian manifold to verify some results.

Harandi [A. A. Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages] introduced the notion of metric-like spaces as a generalization of partial metric spaces and studied some fixed point theorems in the context of the metric-like spaces. In this paper, we utilize the notion of the metric-like spaces to introduce and prove some common fixed points theorems for mappings satisfying nonlinear contractive conditions in partially ordered metric-like spaces. Also, we introduce an example and an application to support our work. Our results extend and modify some recent results in the literature.

This paper is devoted to studying the existence and uniqueness of solutions to the boundary value problems for a impulsive fractional differential equation in Banach spaces. The arguments are based upon the methods of noncompact measure, Banach fixed point theorem and Krasnoselskii?s fixed point theorem. Some examples are given to demonstrate the application of our main results.

[EN] In this paper we introduce and study the concept of strong convergence in fuzzy metric spaces (X, M,*) in the sense of George and Veeramani. This concept is related with the condition Lambda M-t > 0(x, y, t) > 0, which frequently is required or missing in this context. Among other results we characterize the class of s-fuzzy metrics by the strong convergence defined here and we solve partially the question of finding explicitly a compatible metric with a given fuzzy metric., Valentn Gregori acknowledges the support of the Spanish Ministry of Economy and Competitiveness under Grant MTM2015-64373-P (MINECO/FEDER, UE).

In this paper, we establish atomic decompositions for the martingale Hardy-Lorentz spaces. As an application, with the help of atomic decomposition, some interpolation theorems with a function parameter for these spaces are proved.

In this paper, we obtain that if the metric of a three dimensional $(k,\mu)'$-almost Kenmotsu manifold satisfies the Miao-Tam critical condition, then the manifold is locally isometric to either the hyperbolic space $\mathbb{H}^3(-1)$ or the Riemannian product $\mathbb{H}^{2}(-4)\times\mathbb{R}$. Moreover, we also prove that if the metric of an almost Kenmotsu manifold with conformal Reeb foliation satisfies the Miao-Tam critical condition, then the manifold is either of constant scalar curvature or Einstein. Some corollaries of main results are also given.

In this paper, we derive a DDVV-type inequality for submianifolds in a Riemannian manifold of nearly quasi-constant curvature. Moreover, two inequalities involving the Casorati curvature and the scalar curvature are obtained.

In this paper, we proved a known theorem under more weaker conditions dealing with absolute Riesz summability of infinite series involving a quasi-sigma-power increasing sequence. And we applied it to the Fourier series. Some new results are also obtained.

In this paper, we prove that 1/|?|2-harmonic quasiconformal mapping is bi-Lipschitz continuous with respect to quasihyperbolic metric on every proper domain of C\{0}. Hence, it is hyperbolic quasi-isometry in every simply connected domain on C\{0}, which generalized the result obtained in [14]. Meanwhile, the equivalent moduli of continuity for 1/|?|2-harmonic quasiregular mapping are discussed as a by-product.

In this paper, we determine the coefficient bounds for functions in certain subclasses of close-to-convex functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy-Euler-type differential equation of order m. Relevant connections of some of the results obtained with those in earlier works are also provided.

In this paper, the authors investigate a majorization problem for certain subclasses of multivalent meromorphic functions defined in the punctured unit disk U* having a pole of order p at origin. The subclasses under investigation are defined through iterations and combinations of the Liu-Srivastava operator and a meromorphic analogue of the Cho-Kwon-Srivastava operator for normalized analytic function. Several consequences of the main results in form of corollaries are also pointed out.

A mapping $f: X \rightarrow Y $ is statistically sequence covering map if whenever a sequence $\lbrace y_n \rbrace$ convergent to $y$ in $Y,$ there is a sequence $\lbrace x_n \rbrace$ statistically converges to $x$ in $X$ with each $x_n \in f^{-1}(y_n) $ and $ x \in f^{-1}(y).$ In this paper, we introduce the concept of statistically sequence covering map which is a generalization of sequence covering map and discuss the relation with covering maps by some examples. Using this concept, we prove that every closed and statistically sequence-covering image of a metric space is metrizable. Also, we give characterizations of statistically sequence covering compact images of spaces with a weaker metric topology.

In this paper we introduce the set of strictly quasi-Fredholm linear relations and we give some of its properties. Furthermore, we study the connection between this set and some classes of linear relations related to the notions of ascent, essentially ascent, descent and essentially descent. The obtained results are used to study the stability of upper semi-B-Fredholm and lower semi-B-Fredholm linear relations under perturbation by finite rank operators.

In the present paper we are interested in the study of the distance Laplacian eigenvalues of a connected graph with fixed order n and chromatic number x. We prove lower bounds on the distance Laplacian spectral radius in terms of n and x. We also prove results related to the distribution of the distance Laplacian eigenvalues with respect to the values of the chromatic number x. For some of the results, we characterize the extremal graphs, for others, we give examples of extremal graphs.

In this paper, we introduce a new concept of weak G-contraction for multi-valued mappings on a metric space endowed with a directed graph. Endpoint theorem of this mapping is established under some sufficient conditions in a complete metric space endowed with a directed graph. Our main results extend and generalize those fixed point in partially ordered metric spaces. Some examples supporting our main results are also given. Moreover, we apply our main results to obtain some coupled fixed point results in the context of complete metric spaces endowed with a directed graph which are more general than those in partially ordered metric spaces.

In this paper, we consider an initial - boundary value problem for a nonlinear wave equation containing a nonlocal term. Using a high order iterative scheme, the existence of a unique weak solution is proved. Furthermore, the sequence established here converges to a unique weak solution at a rate of order N (N≥2).

In this paper, we propose a method based on generating functions for constructing q-analogues of some discrete type positive linear operators (e.g., q-Lupas, q-Bernstein, q-Meyer-Konig and Zeller and ¨ q-Bleimann-Butzer-Hahn operators etc.). In other words, general operators of the discrete type are constructed, and their respective formulae for central moments are thereby obtained. Finally, through the use of specific generating functions, we are able to provide some relevant exemplary applications of general operators.

Let G? be a signed graph with the underlying graph G and with sign function ? : E(G) ? {?}. In this paper, we characterize the signed graphs with two distinct eigenvalues whose underlying graphs are triangle-free. Also, we classify all 3-regular and 4-regular signed graphs whose underlying graphs are triangle-free and give their adjacency matrices as well.

The Jacobsthal quaternions defined by Szynal-Liana and Wloch [35]. In this paper, we defined some properties of Jacobsthal quaternions. Also, we investigated the relations between the Jacobsthal quaternions which connected with Jacobsthal and Jacobsthal-Lucas numbers. Furthermore, we gave the Binet formulas and Cassini identities for these quaternions.

In this paper, some additive properties of the pseudo Drazin inverse are obtained in a Banach algebra. In addition, we find some new conditions under which the pseudo Drazin inverse of the sum a + b can be explicitly expressed in terms of a, az, b, bz. In particular, necessary and sufficient conditions for the existence as well as the expression for the pseudo Drazin inverse of the sum a+b are obtained under certain conditions. Also, a result of Wang and Chen [Pseudo Drazin inverses in associative rings and Banach algebras, LAA 437(2012) 1332-1345] is extended.

In this paper, the generalizations of Gronwall?s type integral inequalities with singular kernels are established. In applications, theorems on stability estimates for the solutions of the nonliner integral equation and the integral-differential equation of the parabolic type are presented. Moreover, these inequalities can be used in the theory of fractional differential equations.

‎I‎n‎ ‎this‎ ‎paper‎, ‎w‎‎e study the existence of weak solutions for ‎stationary‎‎ fractional reaction-diffusion ‎equations‎‎ ‎with‎ ‎Riemann‎-‎Liouville‎ boundary ‎conditions‎. An‎ appropriate fractional ‎Hilbert‎ space ‎is‎ introduced and a compact embedding theorem demonstrated. ‎Existence results are established using generalized Weierstrass theorem and relatively simple techniques from nonlinear functional analysis‎.

In this paper, we consider an inverse elliptic problem with Neumann type overdetermination and construct a fourth order of accuracy difference scheme for its solution. Stability, almost coercive stability and coercive stability estimates for the solution of difference problem are proved. Later, we construct a fourth order difference scheme for an inverse problem for multidimensional elliptic equation with Neumann type overdetermination and Dirichlet boundary condition. Finally, we illustrate numerical example with descriptions of numeric realization in a two-dimensional case. WOS:000397270800008 2-s2.0-85014474030

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

In this paper, we introduce a new notion of completely semi-weakly hyponormal operator which is a special case of polynomially hyponormal operator. For an one-step backward extension of the Bergman weighted shift, we show that completely semi-weakly hyponormal weighted shifts need not be subnormal. In addition, we provide an example which can serve to distinguish the semi-weak $m$-hyponormality from the semi-weak $m$-hyponormality with positive determinant coefficients for such a shift. Finally we discuss flatness on semi-weakly $m$-hyponormal weighted shifts.

In this paper, based on some biological meaning, triple-negative T cells (TN) and the immature singlepositive T cells (CD3^{−}4^{+}8^{−} and CD3^{−}4^{−}8^{+}) have been introduced into well known Mehr’s non-linear differential equation which is used to describe proliferation, differentiation and death of T cells in the thymus (Modeling positive and negative selection and differentiation processes in the thymus, Journal of Theoretical Biology, 175 (1995) 103-126), and a class of improved nonlinear differential system with seven state variables and time delays has been proposed. Then, by using quasi-steady-state approximation and some classical analysis techniques of functional differential equations, the local and global asymptotic stability of the equilibrium of the system have been analysed. Finally, some numerical simulations are given to summarize the applications of the theoretical results.

In this paper, we introduce regularly generated sequences for double sequence of real numbers, and obtain some Tauberian theorems for (C; 1; 1) summability method using the concept of regularly generated sequence.

In this paper we define the tangential property in partial metric spaces to prove a common fixed point theorems for two pairs of self mappings, which satisfying a generalized weak contractive condition as well as satisfying a generalized contraction, an example is given to illustrate ours results.

In this paper, we obtain some new fixed point theorems for (?,?,?,?) -contractive multi-valued mappings in ?-?-T-complete Menger PM-spaces, which turn out to generalize many results in existing literatures. Some examples are also given to illustrate the definition and support our new results. Moreover, some interesting fixed point results endowed with binary relations or graphs are derived as applications of our main results.

In this paper, we first prove existence of fixed points of generalized nonexpansive mappings in CAT(0) spaces. These are the mappings which satisfy the so-called condition (E). We then approximate them by the ?-convergence and strong convergence using Picard-Mann hybrid iterative process. Our results generalize the corresponding results of many authors.

WOS:000397270800014 In this paper, we investigate the extremal solutions for a class of nonlinear fractional differential equations with order q is an element of (0; 1) by means of monotone iterative technique via initial time different coupled upper and lower solutions.

In this paper, we investigate scattering theory of the impulsive Sturm-Liouville boundary value problem (ISBVP). In particular, we find the Jost solution and the scattering function of this problem. We also study the properties of the Jost function and the scattering function of this ISBVP. Furthermore, we present two examples by getting Jost function and scattering function of the impulsive boundary value problem. Besides, we examine the eigenvalues of these boundary value problems given in examples in detail.

In this paper, some fixed point results of Ciric type in partial b-metric spaces are complemented and generalized. An example is given to support the obtained results.

Let G be a finite group of order pqr where p > q > r > 2 are prime numbers. In this paper, we find the spectrum of Cayley graph Cay(G,S) where S ? G \ {e} is a normal symmetric generating subset.

In this note, we prove the conjecture in the paper [Shang Y. \emph{A central limit theorem for randomly indexed m-dependent random variables.} Filomat 26.4 (2012): 713-717] about the sum of a random number $N_n$ of $m$-dependent random variables. The random number $N_n$ is supposed to converge in probability toward a positive random variable.

In this paper, inspired the very interesting results of Ciric [20], we investigate the existing non-unique fixed points of certain operators in the context of b-metric spaces. Our main results unify and cover several existing results on the topic in the literature.

Very recently, many fixed point results have been introduced in the setting of graphical metric spaces. Due to their intimate links, such works also deal with metric spaces endowed with partial orders. As the reachability relationship in any directed graph (containing all cycles) is a reflexive transitive relation (that is, a preorder), but it is not necessarily a partial order, results on graphical metric spaces are independent from statements on ordered metric spaces. The main aim of this paper is to show that fixed point theorems in the setting of graphical metric spaces can be directly deduced from their corresponding results on measurable spaces endowed with a binary relation. Finally, we also describe the main advantages of involving this last class of spaces.

In the present paper, we introduce the notion of ?-type F-?-contraction and establish related fixed point results in metric spaces. An example is also given to illustrate our main results and to show that our results are proper generalization of Altun et al. (2015), Miank et al. (2015), Altun et al. (2016) and Olgun et al. (2016). We also obtain fixed point results in the setting of partially ordered metric spaces. Finally, an application is given to set up the existence of positive definite solution of non-linear matrix equation.

In this paper we obtain some results concerning the ascent and descent of a quasi-Fredholm relation in a Hilbert space and we analyze the behaviour of a polynomial in a quasi-Fredholm relation in a Hilbert space.

iscan, imdat/0000-0001-6749-0591 WOS: 000428735200005 In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

The classical power sum and alternating power sum identities can be stated as ?m,i=0 sn(i)= 1/n+1 (Bn+1(m+1)- Bn+1), ?m,i=0(-1)i sn (i) = 1/2 ((-1)m En(m+1) + En), where sn(x)=xn is the simplest possible Appell polynomial for the Sheffer pair (1,t). The impetus for this research starts from the question that what if we replace sn(x)=xn by any Appell polynomial. In this paper, we give a generalization of power and alternating power sums to any Appell polynomials.

In this paper, we establish some fixed point theorems in G-metric spaces involving generalized cyclic contractions. Some subsequent results are derived. The presented results generalize many well known results in the literature. Moreover, we provide some concrete examples and an application on the existence and uniqueness of solutions to a class of nonlinear integral equations.

In this paper, we present some sufficient conditions for which a Banach space has normal structure and therefore the fixed point property for nonexpansive mappings in terms of the generalized James, von Neumann-Jordan, Zb?ganu constants, the Ptolemy constant and the Dom?nguez-Benavides coefficient. Our main results extend and improve some known results in the recent literature.

In this paper, we establish strong and ?-convergence theorems of modified three-step iterations for total asymptotically nonexpansive mapping which is wider than the class asymptotically nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and generalize the corresponding results of Chang et al. [Demiclosed principle and ?-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces, Appl. Math. Comput. 219(5) (2012) 2611-2617], Nanjaras and Panyanak [Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. Vol. 2010, Art. ID 268780], and many others.