Some new lacunary $f$-statistical $A$-convergent sequence spaces of order $\alpha$

TL;DR

This paper introduces new lacunary $f$-statistical $A$-convergent sequence spaces of order $ppa$, exploring their properties, relations with ordinary convergence, and connections with Musielak-Orlicz functions.

Contribution

It defines and analyzes novel lacunary $f$-statistical $A$-convergent sequence spaces of order $ppa$, extending existing convergence concepts with respect to lacunary sequences and Musielak-Orlicz functions.

Findings

Established relations between ordinary and module statistical convergence.

Developed properties of the new lacunary $f$-statistically $A$-convergent spaces.

Connected convergence concepts with Musielak-Orlicz functions.

Abstract

We study the concept of density for sets of natural numbers in some lacunary $A$-convergent sequence spaces. Also we are trying to investigate some relation between the ordinary convergence and module statistical convergence for evey unbounded modulus function. Morever we also study some results on the newly defined lacunary $f$-statistically $A$-convergent sequence spaces with respect to some Musielak-Orlicz function.