On strongly almost lacunary statistical $A$-convergence defined by Musielak-Orlicz function

TL;DR

This paper introduces a new class of sequence spaces based on Musielak-Orlicz functions and lacunary statistical convergence, exploring their properties and relationships with existing spaces.

Contribution

It defines strongly almost lacunary statistical $A$-convergence of order $eta$ using Musielak-Orlicz functions and investigates inclusion relations and properties of these spaces.

Findings

Established inclusion relations between new and existing sequence spaces.

Analyzed properties of Musielak-Orlicz functions in the context of these spaces.

Provided conditions for convergence and space characterization.

Abstract

We study some new strongly almost lacunary statistical $A$-convergent sequence space of order $\alpha$ defined by a Musielak-Orlicz function. We also give some inclusion relations between the newly introduced class of sequences with the spaces of strongly almost lacunary $A$-convergent sequence of order $\alpha$. Moreover we have examined some results on Musielak-Orlicz function with respect to these spaces.