On rough $I^*$ and $I^K$-convergence of sequences in normed linear spaces

TL;DR

This paper introduces and studies new concepts of rough $I^*$-convergence and rough $I^K$-convergence in normed linear spaces, extending existing notions and exploring their properties and relationships.

Contribution

It proposes the novel notions of rough $I^*$-convergence and rough $I^K$-convergence, expanding the framework of convergence in normed linear spaces.

Findings

Properties of rough $I^*$-convergence analyzed

Properties of rough $I^K$-convergence examined

Relationships between rough $I$-, $I^*$-, and $I^K$-convergence established

Abstract

In this paper, we have introduced first the notion of rough $I^*$-convergence in a normed linear space as an extension work of rough $I$-convergence and then rough $I^K$-convergence in more general way. Then we have studied some properties on these two newly introduced ideas. We also examined the relationship between rough $I$-convergence with both of rough $I^*$-convergence and rough $I^K$-convergence.