Statistical convergence of order β for generalized difference sequences of fuzzy numbers

Abstract

In this study we introduce the concepts of m −statistical convergence of order β and strong m p −Cesàro summability of order β for sequences of fuzzy numbers by helping many examples. Also, we establish some properties which are valid for sequences of real numbers, but not for sequences of fuzzy numbers.

Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers

“…The essential tenet of statistical convergence is to loosen the restrictions of this condition and to insist that the convergence requirement be valid only for the vast majority of the elements. Later on, this concept and summability theory was associated by several mathematicians ( [1], [5], [6], [9], [10], [13], [14], [18], [19], [22]). Recent years Gadjiev and Orhan [15] broaden the concept of statistical convergence into the ordered statistical convergence.…”

f-statistical convergence of order β for sequences of fuzzy numbers

“…The purpose of this paper is to generalize the study of Bhardwaj [7] and Ç olak [11] applying to sequences of fuzzy numbers so as to fill up the existing gaps in the summability theory of fuzzy numbers. For a detailed account of many more interesting investigations concerning statistical convergence of order α and β, one may refer to ([12], [14], [15], [16], [2], [3], [5]) This paper organizes as follows: In section 2, we give the basic notions which will be used throughout the paper. In section 3, we define the spaces S β (F, f ) and w β (F, f ) , the set of all f −statistically convergent sequences of order β and strong Cesàro summability of order β with respect to an unbounded modulus function f for fuzzy sequences, respectively and establish inclusion relations among the spaces S β (F, f ) for different values of β.…”

“…The purpose of this paper is to generalize the study of Bhardwaj [7] and C ¸olak [11] applying to sequences of fuzzy numbers so as to fill up the existing gaps in the summability theory of fuzzy numbers. For a detailed account of many more interesting investigations concerning statistical convergence of order α and β, one may refer to ( [12], [14], [15], [16], [2], [3], [5])…”

Lacunary statistical convergence of order β in difference sequences of fuzzy numbers

“…The difference spaces ℓ ∞ (∆), c (∆) and c 0 (∆), consisting of all real valued sequences x = (x k ) such that ∆x = ∆ 1 x = (x k − x k+1 ) in the sequence spaces ℓ ∞ , c and c 0 , were defined by Kızmaz [16]. The idea of difference sequences was generalized by Et and Ç olak [10], Altinok [2], Ç olak et al [6], Tripathy and Baruah [25] and many others.…”