Global Optimal Solutions for Proximal Fuzzy Contractions Involving Control Functions

Abdelhamid Moussaoui,Nawab Hussain,Said Melliani,Naeem Saleem

doi:10.1155/2021/6269304

Abdelhamid Moussaoui, Nawab Hussain + Show 2 more

Open Access

https://doi.org/10.1155/2021/6269304

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Abstract

In this study, we introduce new concepts of α − FZ -contraction and α − ψ − FZ -contraction and we discuss existence results of the best proximity points of such types of non-self-mappings involving control functions in the structure of complete fuzzy metric spaces. Our results extend, generalize, enrich, and improve diverse existing results in the current literature.

Highlights

Recent advancements in fixed point theory are one of the central and active research areas of nonlinear functional analysis, which provides a variety of mathematical methods, principles, and techniques for solving a variety of problems arising from various branches of mathematics as well as various fields in science and engineering. e Banach fixed point theorem is considered as one of the most fruitful results in this theory
Khojasteh et al [23] presented an impressive technique to the investigation of fixed point theory by developing the notion of simulation functions, which exhibit a significant unifying power. e idea of simulation functions has been generalized, improved, and extended in different metric spaces
E best proximity theory is another expanding and prominent aspect of fixed point theory which plays a fundamental role in the investigation of requirements that guarantee the existence of an optimal approximate fixed point when the functional equation Lx x has no solution

Summary

Introduction

Recent advancements in fixed point theory are one of the central and active research areas of nonlinear functional analysis, which provides a variety of mathematical methods, principles, and techniques for solving a variety of problems arising from various branches of mathematics as well as various fields in science and engineering. e Banach fixed point theorem is considered as one of the most fruitful results in this theory. In the present study, following this line of research interest, we present a simulation function approach to best proximity point problems in fuzzy metric spaces. Let Ψ be the class of nondecreasing functions ψ: (0, 1] ⟶ (0, 1] fulfilling the following two conditions: (ψ1) ψ is continuous (ψ2) ψ(c) > c for all c ∈ (0, 1) A self-mapping L: Λ ⟶ Λ on a fuzzy metric space (Λ, D, ∗) is called a fuzzy ψ-contractive mapping if

Results

Conclusion