Lacunary I₂-invariant convergence of double sequences of functions on amenable semigroups

Abstract

In this study, we introduce the concept of lacunary I2-invariant convergence, lacunary I∗2-invariant convergence and lacunary I2-invariant Cauchy for double sequences in the topology introduced by random 2-normed spaces. We give the relationships among these concepts and prove some important results