Strongly I–deferred Cesáro summablity and µ-deferred I–statistically convergence in amenable semigroups

Abstract

Abstract: The primary objective of this study is to extend the concept of strongly I-deferred Cesáro
summability and µ-deferred I-statistical convergence on amenable semigroups. Furthermore, under few condi-
tions, we also establish some inclusion-based results. After that, we introduce the µ-deferred I ∗ -statistical con-
vergent, µ-deferred I-statistically pre-Cauchy, and µ-deferred I ∗ -statistically pre-Cauchy functions in amenable
semigroups and prove results based on connection among them. Few counter-examples are also presented to
support our results.