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

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