Note on $f_\lambda$-statistical convergence

TL;DR

This paper explores $_\lambda$-statistical convergence, introduces $f_\lambda$-summability, and investigates their relationships, advancing the understanding of generalized convergence concepts in mathematical analysis.

Contribution

It introduces the concept of $f_\lambda$-summability and examines its relation to $_\lambda$-statistical convergence, expanding the theoretical framework of convergence methods.

Findings

Established properties of $_\lambda$-statistical convergence.

Defined and analyzed $f_\lambda$-summable sequences.

Demonstrated connections between $f_\lambda$-summability and $_\lambda$-statistical convergence.

Abstract

In this article, we study about the $\lambda$-statistical convergence with respect to the density of moduli and find some results related to statistical convergence as well. Also we introduce the concept of $f_\lambda$-summable sequence and try to investigate some relation between the $f_\lambda$-summability and module $% \lambda$-statistical convergence.