On Strong Convergence of Halpern’s Method for Quasi-Nonexpansive Mappings in Hilbert Spaces

Abstract

In this paper, we introduce a Halpern’s type method to approximate common fixed points of a nonexpansive mapping T and a strongly quasi-nonexpansive mappings S, defined in a Hilbert space, such that I − S is demiclosed at 0. The result shows as the same algorithm converges to different points, depending on the assumptions of the coefficients. Moreover, a numerical example of our iterative scheme is given.

Keywords

• approximation algorithm
• fixed point
• variational inequality