On lacunary statistical convergence and lacunary stron Ces\`aro convergence by moduli

TL;DR

This paper completes the study of relationships between various convergence methods, including lacunary statistical and strong Cesàro convergence, using lacunary sequences and density measures modulated by a modulus function.

Contribution

It extends previous work by fully characterizing the connections between these convergence types involving lacunary sequences and modulus functions.

Findings

Established equivalences between lacunary statistical and strong Cesàro convergence.

Generalized convergence concepts using modulus functions.

Unified framework for different convergence methods.

Abstract

Here we fully complete the studies initiated by Vinod K. Bhardwaj and Shweta Dhawan in \cite{hindawi} which relate different convergence methods which involves the classical statistical and the classical strong Ces\`aro convergences by means of lacunary sequences and measures of density in $\mathbb{N}$ modulated by a modulus function $f$.