Common best proximity point theorems under proximal F-weak dominance in complete metric spaces

Abstract

Suppose that A and B are nonempty subsets of a complete metric space $$(\mathcal {M},d)$$ and $$\phi ,\psi :A\rightarrow B$$ are mappings. The aim of this work is to investigate some conditions on $$\phi $$ and $$\psi $$ such that the two functions, one that assigns to each $$x\in A$$ exactly $$d(x,\phi x)$$ and the other that assigns to each $$x\in A$$ exactly $$d(x,\psi x)$$ , attain the global minimum value at the same point in A. We have introduced the notion of proximally F-weakly dominated pair of mappings and proved two theorems that guarantee the existence of such a point. Our work is an improvement of earlier work in this direction. We have also provided examples in which our results are applicable, but the earlier results are not applicable.