CONVERGENCE THEOREMS FOR SEQUENTIALLY ADMISSIBLE PERTURBATIONS OF ASYMPTOTICALLY DEMICONTRACTIVE AND HEMICONTRACTIVE MAPPINGS IN CAT(0) SPACES

Abstract

In this paper, we introduce a new concept of sequentially admissible mappingand sequentially admissible perturbation. Also we construct iteration process correspondingto sequentially admissible mappings. Moreover, we establish theorems of strong conver-gence for the Mann type iterative method(called G ͙ M-algorithm) defined as an uniformly L-Lipschitzian, sequentially admissible perturbation of asymptotically demicontractive mappings and for the Ishikawa type iterative method(called G ͙ I-algorithm) defined as an uniformly L-Lipschitzian, sequentially admissible perturbation of asymptotically hemicontrac-tive mappings to a fixed point in CAT(0) spaces. Finally, we propose an open problem.