On Modulated Lacunary Statistical Convergence of Double Sequences

Abstract

In earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence and strong Cesàro convergence, modulated by a function f (called a modulus function). Such nice structure pivots around the notion of compatible modulus function. In this paper, we will explore such a structure in the framework of lacunary statistical convergence for double sequences and discover that such structure remains true for lacunary compatible modulus functions. Thus, we continue the work of Hacer ¸Senül, Mikail Et and Yavuz Altin, and we fully solve some questions posed by them.