Ideal Deferred Statistical Convergence of Multisequences

Abstract

This paper introduces the concept of deferred statistical convergence of multisequences, extending classical statistical convergence methods to a framework that accommodates repeated elements in multisets. Multisequences, which allow repeated elements within a set, are widely applicable in various fields such as computer science, chemistry, and telecommunications.

The study revisits foundational concepts, including ideal convergence, deferred mean, and statistical convergence, providing a thorough theoretical framework. Main definitions and properties of deferred statistical convergence for multisequences are presented, followed by the introduction of ideal deferred statistical limit superior and inferior, which extend the classical notions of limit points.

Furthermore, the paper establishes several inclusion theorems, demonstrating the relationships between ideal deferred statistical convergence and strong summability within the context of multisequences. Special cases are analyzed under specific conditions, offering insights into the behavior of multisequences. Moreover, the paper introduces original definitions and results regarding ideal deferred statistical cluster and limit points, as well as ideal deferred statistical limit supremum and infimum.

By bridging the gap between classical convergence theories and multisequence analysis, this work provides a new perspective on the study of multisequences and their convergence properties, encouraging further research in this evolving field.