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 {xn } in A such that lim n →∞ || xn − T xn || → 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.