A CONCEPT OF αβ−STATISTICAL CONVERGENCE OF MULTISET SEQUENCE

Abstract

In 2014, Aktuglu [1] first introduced the notion of αβ-statistical
convergence which is more general than the notion of statistical convergence
and lacunary statistical convergence. In this paper, based on this notion, we
introduce the notion of αβ-statistical convergence and αβ-strongly summability for multiset sequences which improves the results in [3, 7]. We investigated
the relations between these two notions and presented several examples corresponding to our results. We also introduce the notion of αβ statistically limit superior and limit inferior for multiset sequences by using the notion of αβ
density which improves the results in [3].