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

Let us consider a nonself nonexpansive mapping T:A→B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T:A\rightarrow B$$\end{document}, 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 {xt}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{x_t\}$$\end{document} 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 {xt}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{x_t\}$$\end{document}.