EXISTENCE OF g-BEST PROXIMITY POINTS OF PROXIMAL F*-WEAK CONTRACTION MAPS.

Let A and B be nonempty subsets of a metric space X. Let S: A → B and g: A → A. In this paper, we prove the existence of best approximate solution x* in the space such that Sx* is as close to gx* as possible. That is, we find the global minimizer of the map x 7→ ρ(gx,Sx) where S is either proximal F*-weak contraction of the first kind or second kind or both, and g is an isometry, in complete metric spaces. Examples are provided to illustrate the validity of our results. [ABSTRACT FROM AUTHOR]