Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications

Abstract

The aim of this paper is to introduce a class of multivalued mappings satisfying a Suzuki type generalized contractive condition in the framework of fuzzy metric spaces and to present fixed point results for such mappings. Some examples are presented to support the results proved herein. As an application, a common fixed point result for a hybrid pair of single and multivalued mappings is obtained. We show the existence and uniqueness of a common bounded solution of functional equations arising in dynamic programming. Our results generalize and extend various results in the existing literature. MSC: 47H10; 47H04; 47H07

Coincidence Point Results for Multivalued Suzuki Type Mappings Using θ-Contraction in b-Metric Spaces

“…It gets more exposure due to the vast applications of fuzzy metric spaces in controlling the noise in data, smoothing the data, and decision-making, but the authors did not pay attention to study the best proximity point theory in fuzzy metric spaces. In 2012, N. Saleem et al investigated best proximity and coincidence point results in fuzzy metric spaces [10][11][12][13][14][15].…”

“…Also, researcher try to study the best proximity point results for multivalued mapping (this was not an easy task). Several authors obtained best proximity points for multivalued mapping, for details, see [13]).…”

Fuzzy b-Metric Spaces: Fixed Point Results for ψ-Contraction Correspondences and Their Application

“…To elaborate the results obtained herein we provide an example that shows the usability of the obtained results.Axioms 2020, 9, 36 2 of 12 some particular types of contractions in the context of "b-metric spaces" (see [28]). In this direction, many researchers studied and extended various well known fixed point results for several types of contractive mappings in the framework of "b-metric spaces" [29][30][31].In general, fixed point theory remained successful in challenging and solving various problems and has contributed significantly to many real-world problems. However, various strong fixed point theorems are proven under strong assumptions.…”

“…Axioms 2020, 9, 36 2 of 12 some particular types of contractions in the context of "b-metric spaces" (see [28]). In this direction, many researchers studied and extended various well known fixed point results for several types of contractive mappings in the framework of "b-metric spaces" [29][30][31].…”

On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces

“…There are also abundant studies on all such topics in classical metric spaces and Banach spaces, either in the fuzzy formalism or not necessarily under the fuzzy formalism, including a lot of research on contractive and non-expansive mappings, self-mappings and, in particular, cyclic proximal mappings. (See, for instance, [26][27][28][29][38][39][40][41][42][43] and the references therein concerning different iterative schemes and their relations to proximal split feasibility, variational inequalities and fixed point problems. There are also recent studies on the generalizations of several types of contractions in [31] with an introduction of the so-called simulation function.…”