{\lambda}-statistical convergent function sequences in intuitionistic fuzzy normed spaces

TL;DR

This paper investigates {}-statistical convergence of function sequences within intuitionistic fuzzy normed spaces, extending classical and fuzzy analysis concepts to this generalized setting.

Contribution

It introduces and studies the properties of {}-statistical convergence for function sequences in intuitionistic fuzzy normed spaces, a novel extension in fuzzy analysis.

Findings

Established basic properties of {}-statistical convergence in intuitionistic fuzzy normed spaces.

Extended classical convergence concepts to the intuitionistic fuzzy setting.

Provided foundational results for future research in fuzzy analysis and convergence.

Abstract

Fuzzy logic was introduced by Zadeh in 1965. Since then, the importance of fuzzy logic has come increasingly to the present.There are many applications of fuzzy logic in the field of science and engineering, e.g. population dynamics (Barros), chaos control (Feng,Fradkov), computer programming (Giles), nonlinear dynamical systems (Hong), etc. The concept of intuitionistic fuzzy set, as a generalization of fuzzy logic, was introduced by Atanassov in 1986. Quite recently Park has introduced the concept of intuitionistic fuzzy metric space, and Saadati and Park studied the notion of intuitionistic fuzzy normed space. Intuitionistic fuzzy analogues of many concept in classical analysis was studied by many authors (Mursaleen, Rsaadati, Jebril, Dinda, etc.). The concept of statistical convergence was introduced by Fast. Mursaleen defined {\lambda}-statistical convergence in Muhammed. Also the concept of statistical convergence was studied in intuitionistic fuzzy normed space in Karakus..Quite recently, Karakaya et al. defined and studied statistical convergence of function sequences in intuitionistic fuzzy normed spaces. Mohiuddine and Lohani defined and studied {\lambda}-statistical convergence in intuitionistic fuzzy normed spaces (Lohani). In this paper, we shall study concept {\lambda}-statistical convergence for function sequences and investigate some basic properties related to the concept in intuitionistic fuzzy normed space.