Approximate best proximity point sequences for C*λ mappings in strictly convex Banach spaces

Abstract

Let A and B be nonempty subsets of a Banach space X and T : A → B be a non-self mapping. An approximate sequence of best proximity points for the mapping T is a sequence {x_n } in A such that lim _n →∞ || x_n − T x_n || → dist(A, B). In the current paper, we survey the existence of approximate best proximity point sequences for single and multivalued  non-self mappings in strictly convex Banach spaces. We also introduce a geometric notion on a nonempty and convex pair of subsets of a Banach space, called semi-Opial condition, and establish some new best proximity point theorems.

Mathematics Subject Classification (2010): 47H10, 47H09, 46B20.