FIXED POINT THEOREMS FOR CONVEX MINIMIZATION PROBLEMS IN COMPLEX VALUED CAT(0) SPACES

Abstract

In this paper, we introduce the concept of a complex valued CAT(0) space and propose a new proximal point algorithm for certain nonlinear operators satisfying rational expressions in the framework of complex valued CAT(0) spaces. We prove existence of fixed point of these nonlinear mappings in such spaces. And we prove strong and ∆-convergence of the iterative sequence generated through our proposed algorithm to the minimizer of a convex function and the fixed point of these mappings. We show that the new iterative algorithm converges faster than the modified Mann-type and Ishikawa-type proximal point algorithms.