On Asymptotically Lacunary Statistical Equivalent Set Sequences

Abstract

This paper presents three definitions which are natural combination of the definitions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, and Wijsman convergence. In addition, we also present asymptotically equivalent (Wijsman sense) analogs of theorems in Patterson and Savaş (2006).

On -Asymptotically Statistical Equivalence of Sequences of Sets

“…(denoted by ∼ ) and simply asymptotically statistically equivalent (Wijsman sense) if = 1 (see [11]). …”

Asymptotically Lacunary Statistical Equivalence of Double Sequences of Sets

“…The concepts of Wijsman asymptotically equivalence, Wijsman asymptotically statistically equivalence, Wijsman asymptotically lacunary equivalence and Wijsman asymptotically lacunary statistical equivalence for sequences of sets were studied by Ulusu and Nuray [24]. In this paper, we get analogous results for double sequences of sets.…”

“…Now, we recall the basic definitions and concepts (See [1,2,3,4,5,9,10,12,13,14,15,16,17,18,21,22,23,24,25,26]). …”

On asymptotically Wijsman lacunary statistical convergence of set sequences in ideal context

“…In [50], Ulusu and Nuray defined the concepts of asymptotically equivalent, asymptotically statistical equivalent and asymptotically lacunary statistical equivalent sequences of sets as follows:…”