MODIFIED PROXIMAL POINT ALGORITHM FOR MINIMIZATION AND FIXED POINT PROBLEM IN CAT(0) SPACES

Abstract

In this paper, we study modified-type proximal point algorithm for approximating a common solution of a lower semi-continuous mapping and fixed point of total asymptotically nonexpansive mapping in complete CAT(0) spaces. Under suitable conditions, some strong convergence theorems of the proposed algorithms to such a common solution are proved.

Keywords

• proximal point algorithm, total asymptotically nonexpansive mapping, fixed point, $\triangle$ convergence, strong convergence, cat(0) space