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It is pointed out that a general theorem presented in Yu Miao and Shoufang Xu's paper has a serious gap. In this small note, a counterexample for this theorem is provided exhibiting a triangular array of real numbers and a sequence of independent identically distributed random variables for which its conclusion fails. An reformulation of Yu Miao and Shoufang Xu's general theorem is performed making this statement true. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [ABSTRACT FROM AUTHOR]

In this paper, we suggest some new and efficient iterative methods for solving nonlinear equations f (x) = 0. These methods are free from derivatives having high order of convergence. We also give some examples to illustrate the efficiency of these methods. Finally, numerical tests confirm the theoretical results and allow us to compare these variants with the classical Steffensen's method. These new methods can be considered as alternative of existing derivative-free methods. [ABSTRACT FROM AUTHOR]

In the present paper, we estimate the rate of convergence of exponential type operators connected with x³ on functions of bounded variation. [ABSTRACT FROM AUTHOR]

In this paper, the initial-value problem for a linear second order delay differential equation is considered. To solve this problem numerically, an appropriate difference scheme is constructed by using the method of integral identities which contains basis functions and interpolating quadrature rules with weight and remainder term in integral form. Besides, the method is proved to be first-order convergent in discrete maximum norm. The numerical illustration provided support the theoretical results. Finally, the proposed method is compared with the implicit Euler method. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and study the concepts of statistical convergence and statistical summability for martingale difference sequences of random variables via deferred weighted summability mean. We then establish an inclusion theorem concerning the relation between these two beautiful concepts. Also, based upon our proposed notions, we state and prove new Korovkin-type approximation theorems with algebraic test functions for a martingale difference sequence over a Banach space and demonstrate that our theorems effectively extend and improves most (if not all) of the previously existing results (in statistical and classical versions). Finally, we present an illustrative example by using the generalized Bernstein polynomial of a martingale difference sequence in order to demonstrate that our established theorems are stronger than its traditional and statistical versions. [ABSTRACT FROM AUTHOR]

The paper studies the existence result for a new class of Kirchhoff elliptic system with variable parameters in the right hand side. Sub-super solutions method are used for proving the main result. Our study is a natural improvement result of our previous one in (Boulaaras et al. in Math. Methods Appl. Sci. 41:5203-5210, 2018). [ABSTRACT FROM AUTHOR]

In this paper we investigate the almost everywhere convergence of two dimensional Marcinkiewicz-like means of two variable integrable functions which is given by... (M|n| ≤ n

In this paper, we study to approximate solutions of quasi-equilibrium problems in Banach spaces, which generalizes equilibrium problems and quasi-variational inequalities. In fact, we prove weak convergence of the sequence generated by the proximal point method to a solution of the quasi-equilibrium problem. Then we show that the generated sequence converges strongly to a solution of the quasi-equilibrium problem. [ABSTRACT FROM AUTHOR]

In this paper, we prove some iterated convergence theorems to fixed points of self mappings satisfying Z-type conditions and Z-operators by considering the base space as a real linear n(> 1)-normed space. We also establish some common fixed point theorems for quadruple of self mappings satisfying certain weak conditions and Φ- contraction. The paper also demonstrates a way to construct convergence and fixed point theorems in real linear n-normed spaces as base space. [ABSTRACT FROM AUTHOR]

In this paper, we construct an iteration scheme involving a hybrid pair of nonexpansive mappings. For this scheme, we prove some convergence theorems in CAT(0) spaces. In process, we remove a restricted condition (also called end-point condition) in previous several existing results. Thus, several relevant results cited in the literature generalize and improve. [ABSTRACT FROM AUTHOR]

The paper is about investigating the uniform convergence conditions of spectral expansions of continuous functions in terms of root functions of a spectral problem with the same eigenparameter in the second-order differential equation and depending on quadratically in one of the boundary conditions on a closed interval. [ABSTRACT FROM AUTHOR]

In this paper, we introduce four new iterative schemes by modifying the shrinking projection method with Ishikawa iteration and S-iteration. The strong convergence theorems are given for obtaining a common fixed point of two G-nonexpansive mappings in a Hilbert space with a directed graph. We also give some numerical experiments for supporting our main theorems and compare convergence rate between them. [ABSTRACT FROM AUTHOR]

In this paper, the author considers the one dimensional initial-boundary problem for a pseudo-parabolic equation with time delay in second spatial derivative. To solve this problem numerically, the author constructs higher order difference method and obtain the error estimate for its solution. Based on the method of energy estimates the fully discrete scheme is shown to be convergent of order four in space and of order two in time. Some numerical examples illustrate the convergence and effectiveness of the numerical method. [ABSTRACT FROM AUTHOR]

Abstract. In this paper, we study Δ-convergence and strong convergence of the sequence generated by the extragradient method for pseudo-monotone equilibrium problems in Hadamard spaces. We first show Δ-convergence of the generated sequence to a solution of the equilibrium problem, then the strong convergence of Halpern regularization method is proved. Finally we give some examples where the main results can be applied. [ABSTRACT FROM AUTHOR]

In this paper, we study q-extension of Mittag-Leffler operators. We establish moments of these operators and estimate convergence results with the help of classical modulus of continuity. Also, we give weighted approximation property and A-statistically convergence of the operators L(β)n,q. [ABSTRACT FROM AUTHOR]

In this paper we define generalized statistical convergence for sequences of sets of order α, 0 < α ⩽ 1 in sense of Wijsman and study some basic properties of this concept. [ABSTRACT FROM AUTHOR]

In this paper we have introduced the concept of geometric convergence of a sequence and determined the necessary and sufficient condition under which convergence follows from geometric convergence of a sequence in multiplicative sense. Corollaries allow this condition to be replaced by multiplicative analogues of Schmidt type slow oscillation condition or Landau type two-sided condition. [ABSTRACT FROM AUTHOR]

In this paper we establish some Tauberian-like conditions in terms of the weighted general control modulo of integer order to retrieve subsequential convergence of a sequence from its boundedness. [ABSTRACT FROM AUTHOR]

In this paper, we will show Tauberian conditions under which λstatistical convergence follows from (V,λ)-statistical convergence. Our results generalize the ones given in [3]. [ABSTRACT FROM AUTHOR]

In this paper we recover convergence and subsequential convergence of a sequence of real numbers regularly generated by another sequence in some sequence spaces under certain conditions. We also give some information about the behavior of a sequence whose generator is given in terms of a moderately divergent sequence. [ABSTRACT FROM AUTHOR]

Let λD(λn) be a non-decreasing sequence of positive real numbers tending to1with λn+1 ⩽λn+1;λ1 D1: In the present paper, we introduce the notion of Ʌ-statistical convergence of order, α, Ʌ-statistical Cauchy sequences of order α in random 2-normed spaces and obtain some results. We display examples which show that our method of convergence is more general in random 2-normed space. [ABSTRACT FROM AUTHOR]

The goal of this paper is to introduce new q-Stancu-Kantorovich operators and to study some of their approximation properties. A convergence theorem using the well known Bohman- Korovkin criterion is proven and the rate of convergence involving the modulus of continuity is established. Furthermore, a Voronovskaja type theorem is also proven. [ABSTRACT FROM AUTHOR]

In the present paper we introduce some new sequence spaces in the n-normed space. We define here some new spaces of double sequences by using the notions of lacunary sequences, difference sequences, almost convergence, sequence of Orlicz functions and statistical convergence. We examine some topological properties of these spaces of double sequences, inclusion relations between these newly defined sequence spaces and establish relation with lacunary statistical convergence. The study of these new sequence spaces provides a tool to deal with convergence problems of double sequences. [ABSTRACT FROM AUTHOR]

In this paper, when approximating a continuos non-negative function on the unit interval, we present an alternative way to the classical Bernstein polynomials. Our new operators become nonlinear, however, for some classes of functions, they provide better error estimations than the Bernstein polynomials. Furthermore, we obtain a simultaneous approximation result for these operators. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of statistical A-summability which is stronger than classical convergence and A-statistical convergence, we obtain a Korovkin-type approximation theorem for double sequences of positive linear operators of two variables from Hw (K) to CB (K). Also, we give an example such that our new approximation result works but its classical and A-statistical cases do not work. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an implicit algorithm for finding a common fixed point of two quasi-nonexpansive multivalued mappings in Banach spaces. We also prove some convergence theorems for the purposed algorithm under some control conditions. [ABSTRACT FROM AUTHOR]

In this paper, we use the notion of ideal to obtain two more general concepts and call them as I-A-statistical convergence and ideal A-summability. We also use the the concept of I-A-statistical convergence to prove a Korovkin type approximation theorem for double sequences of positive linear operators and present an interesting example to show that our Korovkin theorem is stronger than those proved earlier. [ABSTRACT FROM AUTHOR]

Let {X, Xn, n ≥ 1} be a sequence of identically distributed random variables and {ai,n, 1 ⩽ i ⩽ n} be a triangular array of constants. In this short paper, we establish a general almost sure convergence theorem for the weighted sum Sn = ... ai,nXi. Our results improves the works of Sung [14]. Furthermore, almost sure convergence theorems of Sn for negatively associated random variables, martingale difference sequence and ρ-mixing sequence are obtained. [ABSTRACT FROM AUTHOR]

In this paper we introduce the Mittag-Leffler operators, which includes the modified Szász-Mirakjan operators. We obtain the transformation properties and compute the rate of convergence by using modulus of continuity. Furthermore we give the A-statistical approximation theorem for these operators. [ABSTRACT FROM AUTHOR]

The paper is devoted to defining a new general class of linear and positive operators depending on a certain function φ. This new class of linear and positive operators generalizes the Szász-Mirakjan operators. For this new class of operators we establish a convergence theorem and the evaluation of the rate of convergence, in terms of the modulus of continuity. [ABSTRACT FROM AUTHOR]

In this paper we present a new acceleration method for accelerating some numerical sequences of successive approximations that arises in solving certain nonlinear equations. We give a convergence result and some numerical examples to illustrate the abilities of the proposed new acceleration technique. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new integral inequalities for convex and m–convex functions by using a new kernel. The analysis used in the proofs is fairly elementary and based on the classical inequalities. We also give some comparisons and applications to special means for our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the statistical approximation properties of real and complex Post-Widder operators based on q-integers. We also obtain a Voronovskaya-type formula in statistical sense for these operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce q-Szász Schurer operators and calculate their moments. The transformation properties, Korovkin type approximation theorem and rate of convergence of the operators are studied. We further obtain global estimates for q??Szász Schurer operators in terms of some Lipschitz classes. [ABSTRACT FROM AUTHOR]

This study is the continuation of our former work [O. Duman and E. Erkusş, Comput. Math. Appl. 52 (2006) 967-974] in which we obtained a statistical Korovkin-type approximation theorem for a sequence of positive linear operators defined on the space of all real-valued continuous and 2π periodic functions on the real m-dimensional space. In this paper, we compute the statistical rates of this statistical approximation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a class of linear positive operators of discrete type and its statistical approximation properties obtained by using a Bohman-Korovkin type theorem. [ABSTRACT FROM AUTHOR]