In this paper, we define and study λ -statistical convergence in intuitionistic fuzzy normed spaces (IFNS) which provide little better tool to study a more general class of sequences. We also introduce here a new concept, that is, λ -statistical completeness and show that IFNS is λ -statistically complete but not complete.

On generalized statistical convergence in intuitionistic fuzzy normed space

Some approximation theorems VIA Statistical convergence

Some new difference sequence spaces of fractional order and their dual spaces

This paper is devoted to extend the notion of almost convergence and its statistical forms with respect to the difference operator involving (p, q)-gamma function and an increasing sequence $$(\lambda _n)$$
 of positive numbers. We firstly introduce some new concepts of almost $${\Delta }^{[a,b,c]}_{h, \alpha , \beta }(\lambda )$$
 -statistical convergence, statistical almost $${\Delta }^{[a,b,c]}_{h, \alpha , \beta }(\lambda )$$
 -convergence and strong almost $$[{\Delta }^{[a,b,c]}_{h, \alpha , \beta }(\lambda )]_r$$
 -convergence. Moreover, we present some inclusion relations between these newly proposed methods and give some counterexamples to show that these are non-trivial generalizations of existing literature on this topic. We then prove a Korovkin type approximation theorem for functions of two variables through statistically almost $${\Delta }^{[a,b,c]}_{h, \alpha , \beta }(\lambda )$$
 -convergence and also present an illustrative example via bivariate non-tensor type Meyer–Konig and Zeller generalization of Bernstein power series. Furthermore, we estimate the rate of almost convergence of approximating linear operators by means of the modulus of continuity and derive some Voronovskaja type results by using the generalized Meyer–Konig and Zeller operators. Finally, some computational and geometrical interpretations for the convergence of operators to a function are presented.

Generalized Statistically Almost Convergence Based on the Difference Operator which Includes the ( p , q )-Gamma Function and Related Approximation Theorems

Aggregation of infinite sequences

Statistical convergence for sequences of fuzzy real numbers has been studied by various authors. In this paper we study the concept of statistical summability (C, 1) for fuzzy real numbers which for real numbers was introduced by Moricz [18]. We also construct some interesting examples.

Statistical summability(C, 1) for sequences of fuzzy real numbers and a Tauberian theorem

λ-Difference sequence spaces of fuzzy numbers

On some generalized sequence spaces

The idea of difference sequences of real (or complex) numbers was generalized by Et and Colak [Et M, Colak R. On some generalized difference sequence spaces. Soochow J Math 1995; 21(4): 377–86; Colak R, Et M. On some generalized difference sequence spaces and related matrix transformations. Hokkaido Math J 1997; 26(3): 483–92]. In this paper, using the difference operator Δ m and an Orlicz function, we introduce and examine some sequence spaces of fuzzy numbers. We study some of their properties like completeness, solidity, symmetricity, etc. We also give some relations related to these spaces.

Hifsi Altinok

Papers

Statistical summability(C, 1) for sequences of fuzzy real numbers and a Tauberian theorem

λ-Difference sequence spaces of fuzzy numbers

On some generalized sequence spaces

Generalized difference sequences of fuzzy numbers

On λ-statistical convergence of difference sequences of fuzzy numbers