Some new $I_\lambda$-lacunary statistical convergence

TL;DR

This paper introduces new sequence spaces based on $I_$-lacunary statistical convergence using Musielak-Orlicz functions, exploring their properties, relations, and applications in topological groups.

Contribution

It defines novel $I_$-lacunary statistically convergent sequence spaces of order , establishing their properties and relations with other summability methods.

Findings

Established inclusion relations between new sequence spaces and existing ones.

Analyzed $I_$-lacunary statistical convergence in topological groups.

Proved important inclusion theorems for the new sequence spaces.

Abstract

In this paper, we introduce some new $I_\lambda$-lacunary statistically convergent sequence spaces of order $\alpha$ defined by a Musielak-Orlicz function. We study some relations between $I_\lambda$-lacunary statistically convergence with lacunary $I_\lambda$-summable sequences. Moreover we also study about the $I_\lambda$-lacunary statistically convergence of sequences in topological groups and give some important inclusion theorems.