Prešić Type Nonself Operators and Related Best Proximity Results

Abstract

The purpose of this article is to discuss the existence of best proximity points for Pre s ˇ i c ´ -type nonself operators, say T : A k → B . We also give several examples to support our results. As a consequence of our results, we have provided some interesting formulations of Pre s ˇ i c ´ fixed point results.

Fixed Point Results for Multivalued Prešić Type Weakly Contractive Mappings

“…Recently, Alecsa [21] introduced Prešić convex contraction and obtained the unique fixed point in the setup of metric spaces. Ali et al [22] obtained the best proximity results of nonself operators in the metric space structure. Babu et al [23] proved the fixed point results of Prešić type mapping in b-Dislocated metric spaces.…”

Interpolative Prešić Type Contractions and Related Results

“…). e existence of such points of nonself maps has been discussed by several researchers in different ways, for example, Caballero et al [22] studied the existence of best proximity points for nonself maps satisfying Geraghty contraction and P-property in metric spaces, Bilgili et al [23], Aydi et al [24], and Pitea [25] extended the work of Caballero et al [22] by introducing generalized Geraghty contraction, ψ-Geraghty contraction and generalized almost θ-Geraghty contraction for nonself maps, Basha and Shahzad [26] and Basha [27] defined proximal-type contractions to study the existence of best proximity points, Jleli and Samet [28] defined α-ψ-proximal contraction to ensure the existence of best proximity points, Jleli et al [29] and Aydi et al [30] defined generalized α-ψ-proximal contractions to extend the work of Jleli and Samet [28], Abkar and Gabeleh [31] and Kumam et al [32] studied the existence of best proximity points for multivalued nonself maps in metric spaces, Ali et al [33] defined implicit proximal contractions, Sahin et al [34] defined proximal nonunique contraction, and Ali et al [35] studied the existence of best proximity points for Prešić type nonself operators satisfying proximal type contractions.…”

Existence theorem for integral inclusions by a fixed point theorem for multivalued implicit-type contractive mappings

“…Controlled contractions are used in [5] in order to obtain best proximity properties. [6] is devoted to best proximity results for Prešić-type operators. Generalized proximal contractive mappings are developed in [11], while [18] refers to global optimal solutions.…”