Approximation of Common Solutions to Proximal Split Feasibility Problems and Fixed Point Problems in Hilbert Spaces: Cholatis Suanoom, Wongvisarut Khuangsatung - Team, Support (Thai Journal of Mathematics, 2018)
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.