Iterative algorithms for finding minimum-norm fixed point of a finite family of nonexpansive mappings and applications

Abstract

This paper deals with iterative methods for approximating the minimum-norm common fixed point of nonexpansive mappings. The proposed cyclic iterative algorithms and simultaneous iterative algorithms combined with a relaxation factor, which make them more flexible to solve the considered problem. Under certain conditions on the parameters, we prove that the sequences generated by the proposed iteration scheme converge strongly to the minimum-norm common fixed point of a finite family of nonexpansive mappings. Furthermore, as applications, we obtain several new strong convergence theorems for solving the multiple-set split feasibility problem which has been found application in intensity modulated radiation therapy. Our results extend and improve some known results in the literature.