MEAN CONVERGENCE THEOREMS FOR ASYMPTOTICALLY DEMICONTRACTIVE MAPPINGS IN THE INTERMEDIATE SENSE

Abstract

Recently, Olaleru and Okeke [19] introduced the class of asymptotically demicon- tractive mappings in the intermediate sense as a generalization of the class of asymptotically demicontractive mappings. The authors proved some convergence theorems for this class of nonlinear mappings in Hilbert spaces (see, [19]). The purpose of this paper is to continue the study of this class of nonlinear mappings. We prove some fixed point theorems for the class of asymptotically demicontractive mappings in the intermediate sense. We also prove some mean convergence theorems for this class of mappings in Hilbert spaces.