Fixed point results via extended $\mathcal{FZ}$-simulation functions in fuzzy metric spaces

Abstract

In this paper, we introduce a new class of control functions, namely extended $\mathcal{FZ}$ FZ -simulation functions, and employ it to define a new contractive condition. We also prove some new fixed and best proximity point results in the context of an M-complete fuzzy metric space. The presented theorems unify, generalize, and improve several existing results in the literature.

Best Proximity Point Results via Simulation Function with Application to Fuzzy Fractional Differential Equations

“…They streamline the proof process by introducing auxiliary functions, thereby enhancing the manageability of analysis and facilitating more elegant and concise proofs. This approach is exemplified in works such as those by [2][3][4][5][6][7][8] and references therein.…”

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.…”

On Principal Fuzzy Metric Spaces

“…Several concepts of convergent sequences have been introduced in our fuzzy context (see [9][10][11] and references therein). In particular, a weaker concept than convergence called p-convergence (Definition 2) was introduced by D. Mihet in [12] devoted to fixed point theory, which is currently a topic of high activity in this context (see, for instance, [13][14][15][16][17][18][19]).…”