Algorithm for approximating common fixed points of family of strictly pseudo-contractive mappings in Hilbert spaces

Abstract

It is our purpose in this paper to construct and study a Halpern-type algorithm with inertial and error terms for approximating common fixed points of strictly pseudo-contractive mappings in the framework of real Hilbert spaces. We prove strong convergence theorem for the sequence generated by the algorithm under certain mild conditions on the control sequences. Numerical examples are given to illustrate the effectiveness of this algorithm. Our result is intended to complement and extend some well known results in the literature.