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In this paper we will prove the Korovkin type theorem for new modified Szász-Mirakyan operators via A-statistical convergence and power summability method. Also we give the rate of the convergence related to the summability methods and in the last section we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss-Voronovskaya type theorem. [ABSTRACT FROM AUTHOR]

In this paper, which deals essentially with various summability concepts and summability techniques and shows how these concepts and techniques lead to a number of approximation results, we have used the new concept of weighted A -summability proposed by Mohiuddine (2016) and introduced the notions of statistically weighted B -summability and weighted B -statistical convergence with respect to the weighted regular method. We then prove a Korovkin type approximation theorem for functions of two variables and also present an example via generalized Meyer-König and Zeller type operator to show that our proposed method is stronger than its classical and statistical versions. Furthermore, the rate of convergence of approximating positive linear operators are estimated by means of the modulus of continuity and some Voronovskaja type results are investigated. Computational and geometrical approaches to illustrate some of our results are also presented. [ABSTRACT FROM AUTHOR]

Fuzzy set theory has entered into a large variety of disciplines of sciences, technology and humanities having established itself as an extremely versatile interdisciplinary research area. Accordingly different notions of fuzzy structure have been developed such as fuzzy normed linear space, fuzzy topological vector space, fuzzy sequence space etc. While reviewing the literature in fuzzy sequence space, we have seen that the notion of Tauberian theorems for the Euler-Nörlund mean-convergent sequences of fuzzy numbers has not been developed. In the present paper, we introduce some new concepts about statistical convergence of sequences of fuzzy numbers. The main purpose of this paper is to study Tauberian theorems for the Euler-Nörlund mean-convergent sequences of fuzzy numbers and investigate some other kind of convergences named Euler-Nörlund mean-level convergence so as to fill up the existing gaps in the literature. The results which we obtained in this study are much more general than those obtained by others. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of almost statistical convergence of generalized difference sequences of fuzzy numbers involving lacunary sequences. We give the relations between the lacunary strongly almost Cesàro type convergence and lacunary almost statistical convergence. Furthermore, we study some of their properties like completeness, solidity, symmetricity etc. We also give some inclusion relations related to these classes. [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 propose to introduce a new Λ 2 -weighted statistical convergence. Based upon this definition, we prove some Korovkin type theorems. We also find the rate of the convergence for this kind of weighted statistical convergence and derive some Voronovskaya type theorems. [ABSTRACT FROM AUTHOR]

In this paper criterion for L1-convergence of a certain cosine sums with quasi hyper-convex coefficients is obtained. [ABSTRACT FROM AUTHOR]

We introduce the Λ 2-strong convergence of numerical sequences and with it we generalize the concept of Λ-strong convergence of the results published by F. Móricz [2]. [ABSTRACT FROM AUTHOR]

We introduce the spaces of A(λ)-null, A(λ)-convergent, and A(λ)-bounded sequences. We examine some topological properties of the spaces and give some inclusion relations concerning these sequence spaces. Furthermore, we compute α-, β-, and γ-duals of these spaces. Finally, we characterize some classes of matrix transformations fromthe spaces of A(λ)-bounded and A(λ)-convergent sequences to the spaces of bounded, almost convergent, almost null, and convergent sequences and present a Steinhaus type theorem. [ABSTRACT FROM AUTHOR]