Best proximity results for Suzuki and convex type contractions

Abstract

The aim of the paper is to introduce new Suzuki and convex type contractions and prove new best proximity results for these contractions in the setting of a metric space. As applications, we deduce similar results for such type of contractions in partially ordered metric spaces and derive new Suzuki type fixed point results. An illustrative example is provided here to highlight our findings.

On the existence of coupled best proximity point and best proximity point for Suzuki type alpha^+-theta-proximal multivalued mappings

“…(i) The results proved in Section 3 generalize the corresponding results of Suzuki [24], Hussain et al [6] and many others. They also enrich and develop existing conclusions on coupled best proximity point [11,23].…”

“…The existence theorems of coupled best proximity points for twovariable α + -θ-proximal multivalued mappings with the hypothesis of continuity or regularity and the best proximity point results for one-variable α + -θ-proximal multivalued mappings with the hypothesis of continuity or regularity are established, respectively. These more generalized results extend and generalize the main results of Hussain et al, Nantadilok, and Jleli et al in the literatures [6,7,11,23,24]. We also provide an example to show the generality and effectiveness of our results.…”

“…Hussian et al [6] established existence theorem for best proximity points of Suzuki type α + -θ-proximal mappings with continuity assumption or regularity on the mappings. (ii) T is proximal α + -admissible;…”

“…In Section 2, we present some preliminaries and recall the results for α + -θ-proximal single-valued mappings. In Section 3, inspired and motivated by Hussain et al [6], Sintunavarat et al [23], Jleli et al [7], and Nantadilok [11], we define the notion of α + -θ-proximal multivalued mapping for one-variable and two-variable and explore the best proximity point theorem and the coupled best proximity point theorem for the class of α + -θ-proximal multivalued mappings in this paper. The existence theorems of coupled best proximity points for twovariable α + -θ-proximal multivalued mappings with the hypothesis of continuity or regularity and the best proximity point results for one-variable α + -θ-proximal multivalued mappings with the hypothesis of continuity or regularity are established, respectively.…”

“…Redjel et al [13] introduced a concept of (α, ψ)-Meir-Keeler-Khan mappings, we also defined the class of (α, ψ)-Meir-Keeler-Khan multivalued mappings recently [25]. Hussain et al [6] introduced the concept of proximal α + -admissible and introduced new Suzuki type contractions and proved new best proximity results for these contractions in the setting of a metric space, they dealt with best proximity theorems for Suzuki contractions involving the θ function which was introduced by Jleli and Samet [7]. Sintunavarat and Kumam [23] introduced the concept of coupled best proximity point and proved the coupled best proximity theorem for involving cyclic contractions.…”