Tauberian theorems for statistical Ces\`{a}ro and statistical logarithmic summability of sequences in intuitionistic fuzzy normed spaces

TL;DR

This paper introduces new Tauberian theorems linking statistical Cesàro and logarithmic summability to convergence in intuitionistic fuzzy normed spaces, expanding the understanding of sequence summability in fuzzy contexts.

Contribution

It establishes novel Tauberian conditions for statistical summability methods in intuitionistic fuzzy normed spaces, including higher order cases and convergence criteria.

Findings

Tauberian conditions for statistical Cesàro summability imply convergence in IFNS.

Tauberian conditions for statistical logarithmic summability imply convergence in IFNS.

Results extend to higher order summability methods and convergence of statically convergent sequences.

Abstract

We define statistical Ces\`{a}ro and statistical logarithmic summability methods of sequences in intuitionistic fuzzy normed spaces($IFNS$) and give slowly oscillating type and Hardy type Tauberian conditions under which statistical Ces\`{a}ro summability and statistical logarithmic summability imply convergence in $IFNS$. Besides, we obtain analogous results for the higher order summability methods as corollaries. Also, two theorems concerning the convergence of statically convergent sequences in $IFNS$ are proved in the paper.