Best proximity points for α–ψ-proximal contractive type mappings and applications

Let A and B be two nonempty subsets of a metric space (X,d). A best proximity point of a non-self-mapping T:A→B is a point x⁎∈A satisfying the equality d(x⁎,Tx⁎)=d(A,B), where d(A,B)=inf{d(a,b):a∈A,b∈B}. In this paper, we introduce a new concept of α–ψ-proximal contractive type mappings and establish best proximity point theorems for such mappings in complete metric spaces. Several applications and interesting consequences of our obtained results are presented.

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