Approximation of Common Solutions to Proximal Split Feasibility Problems and Fixed Point Problems in Hilbert Spaces

Cholatis Suanoom, Wongvisarut Khuangsatung

Abstract

In this paper, a new iterative algorithm is proposed for  finding the minimum-norm solution of a  proximal split minimization problem and   fixed point problem of quasi-nonexpansive mappings in Hilbert spaces.  Under suitable conditions, it is proved that  the sequence generated by the proposed algorithm converges strongly to a common solution of the two above described problems. The iterative algorithm are proposed in such a way that the selection of the step-sizes does not need any prior information about the operator norm.