Global Optimal Solutions for Proximal Fuzzy Contractions Involving Control Functions

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.

Fixed Point Results for New Types of Fuzzy Contractions via Admissible Functions and FZ -Simulation Functions

“…then Definition 12 yields the concept of F Z-contraction ( [8,19]), even the definition of the fuzzy contractive mapping introduced in [5] by taking…”

“…Accordingly, many researchers extended and enriched this notion in various distinct metric spaces (see [11,14,[16][17][18]). In 2018, inspired by the aforementioned approach, Melliani and Moussaoui [8,19] proposed a new type of fuzzy contractions, called F Z-contraction in the context of fuzzy metric spaces and showed that this new form of contractions can also yield a unique point of view for various well-known concepts such as fuzzy contractions [5], fuzzy ψ-contractions [6], and fuzzy H-contractions [7]. Other remarkable results were presented in [10] where the concept of admissible mappings was initiated to include numerous and diverse contractions.…”

Fixed Point Results via G-Transitive Binary Relation and Fuzzy L-R-Contraction

“…The concept of ψ-contractive mappings was later proposed by Mihet [10]. Recent research by Abdelhamid Moussaoui et al [11] (see also [12]) introduced the idea of F Z-contractions and initiated a fuzzy metric version of the simulation function technique. Further research consequences of numerous forms of contractions in fuzzy metric spaces and other structures are provided in [11][12][13][14][15][16][17][18] In this study, we introduce the idea of a fuzzy L-R-contraction and develop some fixed point results encompassing the G-transitive binary relation and fuzzy L-simulation functions by using appropriate hypotheses on the fuzzy metric space equipped with a binary relation.…”