Mixed Simultaneous Iterative Algorithms for the Extended Multiple-Set Split Equality Common Fixed-Point Problem with Lipschitz Quasi-Pseudocontractive Operators

Abstract

In this paper, we study a kind of extended multiple-set split equality common fixed-point problem with Lipschitz quasi-pseudocontractive operators, which is an extension of multiple-set split equality common fixed-point problem with quasi-nonexpansive operator. We propose two mixed simultaneous iterative algorithms, in which the selecting of the stepsize does not need any priori information about the operator norms. Furthermore, we prove that the sequences generated by the mixed simultaneous iterative algorithms converge weakly to the solution of this problem. Some numerical results are shown to illustrate the feasibility and efficiency of the proposed algorithms.