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

AMS Subject Classification:

• 47J20
• 47J25
• 49J10
• 65J15