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

Abstract

In this paper, we introduce two new concepts, generalized α-η-FZ-contraction and modified α-η-FZ-contraction, which unify several types of contractions in the context of fuzzy metric spaces. We discuss the existence and uniqueness results of such mappings in the setting of a complete fuzzy metric space in the sense of George and Veeramani and present several significant consequences of our obtained results by using variant examples for FZ-simulation functions and admissible mappings. Some examples are provided to illustrate the usability of our main results.

Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems

“…Nonetheless, fuzzy metrics show some differences compared with classical ones which still make their study of interest nowadays. On the one hand, they differ in some purely metric topics as completeness or fixed point theory, which are two active topics of research in the literature (see, for instance, the following recent references [5][6][7][8][9][10][11]). On the other hand, fuzzy metrics have been successfully used, compared with their classical counterparts, in engineering problems such as model estimation, modelling multi-agent systems or image filtering (see, for instance, [12][13][14][15][16][17] and references therein).…”

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

“…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. The results combine, generalize, and enhance a number of prior research results.…”

A Common Fixed-point Theorem of Mappings on S-metric Spaces

“…It had an importance and role in Functional Analysis, Differential Equations, Physics for its applicable sides. During the years, many authors ( [2][3][4][5]) have worked on this direction defining new contractions and new spaces by generalizing the results of Banach [1].…”