Global best approximate solutions for set-valued cyclic α-F-contractions

Abstract

In this paper, we introduce the concepts of multivalued cyclic α-F contraction and triangular α-orbital admissible mappings. We use these concepts to find global best approximation solutions in a metric space with proximally complete property. We also provide some nontrivial examples to support our results. As an application, we obtain best proximity point results in partially ordered metric spaces and best proximity point theorems for single-valued mappings. We also prove fixed point results for multivalued and single-valued α-type F-contractions.

Contraction Mappings and Applications

“…0 such that for all x, y ∈ X , ðÞ , then T has a fixed point in X . For more in this direction, see, [28][29][30][31]. Here, we give the concept of multivalued α-F-weak-contractions and prove some fixed point results.…”

Existence of Best Proximity Point with an Application to Nonlinear Integral Equations

“…Following the proof of eorem 1, the sequence ′ u n 􏼚 􏼛 is Cauchy and converges to some ′ u * in (ℵ, ℘). From our assumption and using (12), there exists a…”

“…Many authors have refined the concept of ϱ-admissible mappings developed by Samet [10] for proximal mappings (see [11,12]). Definition 2.…”

Admissible Hybrid Z -Contractions in Extended b -Metric Spaces

“…The concept of a b-metric space was accomplished by the works of Bourbaki [2], Bakhtin [3], and Czerwik [4]. Subsequently, several articles have appeared in literature which dealt with the fixed point theorems by taking into account more general forms, of a metric spaces, i.e., b-metric space, see [5], and the applications of relaxed triangular inequalities, like NEM (nonlinear elastic matching), ice floes, etc., were also utilized in various directions [6,7]. Following the idea of b-metric spaces, a number of authors have presented several results in this direction, see [8,9].…”