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

The primary objective of this study is to extend the concept of strongly I-deferred Ces?ro summability and ?-deferred I-statistical convergence on amenable semigroups. Furthermore, under few conditions, we also establish some inclusion-based results. After that, we introduce the ?-deferred I*-statistical convergent, ?-deferred I-statistically pre-Cauchy, and ?-deferred I*-statistically pre-Cauchy functions in amenable semigroups and prove results based on connection among them. Certain counter-examples are also presented to support our results.