Lacunary statistical convergence of order beta in difference sequences of fuzzy numbers

TL;DR

This paper introduces new spaces of fuzzy number sequences based on lacunary statistical convergence of order beta, using generalized difference operators and explores their relationships and inclusion properties.

Contribution

It defines novel sequence spaces of fuzzy numbers incorporating lacunary statistical convergence of order beta and establishes their interrelations and inclusion theorems.

Findings

Defined new sequence spaces for fuzzy numbers using lacunary statistical convergence

Established relations between the newly defined spaces

Proved inclusion theorems involving these spaces and modulus functions

Abstract

In this paper, we define the spaces $N_{\theta }^{\beta }\left( p,F,\Delta ^{m}\right) ,$ $S_{\theta }^{\beta }\left( F,\Delta ^{m}\right) ,$ $w_{p}^{\beta }\left( F,\Delta ^{m}\right) $ for sequences of fuzzy numbers using generalized difference operator $\Delta ^{m}$ and a lacunary sequence $\theta $ and give some relations between them, where $ \beta \in \left( 0,1\right] $ and $p>0$. Furthermore, in the last section of paper, some inclusion theorems are presented related to the spaces $ S_{\theta }^{\beta }\left( F,\Delta ^{m}\right) $ and $w_{p}^{\beta }\left( \theta ,f,F,\Delta ^{m}\right) $ according to modulus function $f$.