Split feasibility and fixed-point problems for asymptotically quasi-nonexpansive mappings

The purpose of this paper is to introduce and analyze a weakly convergent theorem by using the regularized method and the relaxed extragradient method for finding a common element of the solution set Gamma of the split feasibility problem and Fix(T) of fixed points of asymptotically quasi-nonexpansive mappings T in the setting of infinite-dimensional Hilbert spaces. Consequently, we prove that the sequence generated by the proposed algorithm converges weakly to an element of Fix(T) boolean AND Gamma under mild assumptions.