Best Proximity Point forα-ψ-Proximal Contractive Multimaps

Abstract

We extend the notions ofα-ψ-proximal contraction andα-proximal admissibility to multivalued maps and then using these notions we obtain some best proximity point theorems for multivalued mappings. Our results extend some recent results by Jleli and those contained therein. Some examples are constructed to show the generality of our results.

Common best proximity results for multivalued proximal contractions in metric space with applications

“…Our results generalize and improve the results of Ali et al [6], Jungck ([18], [19]), Samet et al [29], and Hussain et al [17].…”

“…When η(z 1 , z 2 ) = 1 for all z 1 , z 2 ∈ A, Definition 2.7 reduces to Definition 10 in [6]. As the condition 1 is more general than the inequality (1.1) (see Remark 3.5 in [5]), so Corollary 2.9 extends Theorem 13 in [6].…”

“…A well-known principle that guarantees a unique fixed point solution is the Banach contraction principle [9]. Over the years, this principle has been generalized Definition 1.5 ( [6]). Let A and B be two nonempty subsets of a metric space (X , d).…”

On the weakly(α, ψ, ξ)-contractive condition for multi-valued operators in metric spaces and related fixed point results

“…For more details of fixed point results and recently related results by using the concepts of˛-admissible single valued and˛-admissible multi-valued mappings, one can refer to [8][9][10][11][12][13][14][15][16] and references therein.…”

A new concept of (α,Fd )-contraction on quasi metric space

“…Various fixed point results for α-admissible mappings and F -contractions on complete metric space can be found in [3,10,12,13,14,15] and [4,6,7,9,21,22,27], respectively.…”