New Types of Convergence on Time Scales

TL;DR

This paper introduces new types of convergence, specifically I-convergence and I*-convergence, for functions on time scales, extending to statistical convergence using ideals on time scales.

Contribution

It proposes novel convergence concepts on time scales, expanding the theoretical framework for analyzing functions in this context.

Findings

Defines I-convergence and I*-convergence on time scales

Extends the concept to statistical convergence on time scales

Provides a new perspective for convergence analysis in time scale calculus

Abstract

This paper is discussing about the notion of some new types of convergences namely $I$-convergence and $I^*$-convergence of a $\Delta$-measurable function $f$ on time scales $T$ by considering ideal on time scales $T$. This idea is further extended to the notion of statistical convergence of a $\Delta$-measurable function $f$ on time scales $T$.