Tauberian theorems for weighted means of double sequences in intuitionistic fuzzy normed spaces

TL;DR

This paper introduces a new weighted mean summability method for double sequences in intuitionistic fuzzy normed spaces and establishes conditions under which summability implies convergence, extending known Tauberian results.

Contribution

It develops necessary and sufficient Tauberian conditions for weighted mean summability in intuitionistic fuzzy normed spaces, advancing the theory of fuzzy sequence convergence.

Findings

Established Tauberian conditions for weighted mean summability in IFNS.

Extended known summation methods to the context of intuitionistic fuzzy spaces.

Provided criteria for when summability implies convergence in this fuzzy setting.

Abstract

We define weighted mean summability method of double sequences in intuitionistic fuzzy normed spaces($IFNS$), and obtain necessary and sufficient Tauberian conditions under which convergence of double sequences in $IFNS$ follows from their weighted mean summability. This study reveals also Tauberian results for some known summation methods in the special cases.