I-Statistical Rough Convergence of Order α

Abstract

The aim of this paper is to define the concept of I-statistical (I-st) rough convergence of order α (0 < α ≤ 1). It proposes the concept of I-st bounded of order α. Moreover, the necessary and sufficient condition for a sequence (x_k) to be I-st bounded of order α is studied. In addition, the necessary and sufficient condition for a sequence (x_k) to be I-st convergent of order α is examined. Finally, the need for further research studies is discussed.

Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Metric Spaces

“…Fast [1] and Steinhaus [2] have established this concept separately in 1951. Many mathematicians particularly Salat [3], Freedman and Sember [4], Fridy [5], Connor [6], Kolk [7], Fridy and Orhan [8], and Bulut and Or [9], have contributed to the development of statistical convergence. Pringshem [10] has introduced the convergence and Cauchy sequence of double sequences.…”

Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces

“…Furthermore, Malik and Maity [7,8] have studied the concepts of rough convergence and rough statistical convergence of double sequences in normed linear spaces, respectively. Besides, many studies on these concepts have been conducted [9][10][11].…”

Rough Statistical Convergence in L-Fuzzy Normed Spaces

“…Fast [5] and Steinhaus [6] independently defined a new type of convergence called statistical convergence, a generalization of classical convergence. Moreover, many valuable works on statistical convergence have been done so far, and many properties have been given [7], [8], [9], [10], [11], [12], [13], [14]. On the other hand, Phu [15] introduced the concept of rough convergence, a generalization of statistical convergence, infinite-dimensional linear spaces.…”