Generalization of best proximity points theorem for non-self proximal contractions of first kind

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The primary objective of this paper is the study of the generalization of some results given by Basha (Numer. Funct. Anal. Optim. 31:569–576, 2010). We present a new theorem on the existence and uniqueness of best proximity points for proximal β-quasi-contractive mappings for non-self-mappings $S:M\rightarrow N$ and $T:N\rightarrow M$ . Furthermore, as a consequence, we give a new result on the existence and uniqueness of a common fixed point of two self mappings.

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