Algorithms for common best proximity points of the global minimization problem in Hilbert spaces

Abstract

Best proximity point of nonlinear mappings can be viewed as a global minimization problem. In this paper, we introduce and analyze a new algorithm for finding a common best proximity point of two nonself nonexpansive mappings in a real Hilbert space. Weak and strong convergence theorems of the proposed algorithm are established under some suitable conditions. Some applications for variational inequality problems and convex minimization problems and some numerical examples supporting our main results are also presented.