On weak $I^K$-Cauchy sequences in normed spaces

TL;DR

This paper introduces and explores the properties of weak $I^K$-Cauchy sequences in normed spaces, generalizing existing concepts and analyzing their relationships and divergence behaviors.

Contribution

It extends the theory of weak $I^*$-Cauchy sequences by defining weak $I^K$-Cauchy sequences and examining their properties and relationships.

Findings

Established the relationship between weak $I$-Cauchy and weak $I^K$-Cauchy sequences.

Analyzed weak* $I^K$-Cauchy conditions and divergence of sequences.

Generalized the concept of Cauchy sequences in the context of $I^K$-ideals.

Abstract

In this paper, we study on weak $I^K$-Cauchy condition as a generalization of weak $I^*$-Cauchy condition in a normed space. We investigate the relationship between weak $I$-Cauchy and weak $I^K$-Cauchy sequences using $AP(I,K)$-condition. Also we study on weak* $I^K$-Cauchy condition and weak $I^K$-divergence of sequences in the same space.