On I-lacunary statistical convergence of order α of sequences of sets

Abstract

The idea of I−convergence of real sequences was introduced by Kostyrko et al.

Some Results on Wijsman Ideal Convergence in Intuitionistic Fuzzy Metric Spaces

“…Moreover, statistical convergence, ideal convergence, and different properties of sequences in intuitionistic fuzzy normed spaces were examined by Mursaleen et al [19][20][21]. Also one can refer to Sengül and Et [22], Sengül et al [23], Et and Yilmazer [24], Mohiuddine and Alamri [25], and Mohiuddine et al [26,27].…”

Wijsman asymptotical I_2-statistically equivalent double set sequences of order η

“…More study on the concepts of convergence or asymptotical equivalence for real sequences or set sequences can be found in [25,26,27,28,29,30,31,32,33,34,35].…”

A variation on strongly ideal lacunary ward continuity

“…An ideal I is called non-trivial if I = 2 N , and an ideal I is said to be admissible if I ⊃ {{n} : n ∈ N}. A non-empty family of sets F ⊆ 2 X is said to be a filter of X if and only if (i) φ / ∈ F, (ii) A, B ∈ F implies A ∩ B ∈ F and (iii) A ∈ F, A ⊂ B implies B ∈ F. The concept of ideal convergence (or I-convergence) of real sequences was introduced by Nuray and Ruckle in [31] who called it generalized statistical convergence as a generalization of statistical convergence which is a generalization of ordinary convergence ( [25], [28], [34], [26], [4], [7], [8], [22], [37], [38], [6]), and also independently by Kostyrko, Salát, and Wilczyński in [29]. Some further results connected with the notion of the I-convergence can be found in ( [24], [30], [35], [32], [33], [40], [10], [11]).…”