Strong convergence of approximants to best proximity points of nonself nonexpansive mappings

Abstract

Let us consider a nonself nonexpansive mapping $$T:A\rightarrow B$$, where A and B are nonempty subsets of a real Hilbert space H. It is worth mentioning that the sequence of iteration is meaningless for this type of nonself mappings. We introduced Browder-type net $$\{x_t\}$$ in A for T and established necessary and sufficient conditions for the existence of a best proximity point of T in terms of the net $$\{x_t\}$$.