A Strong Convergence Theorem for Solving the Split Equality Fixed Point Problem

Abstract

In this paper, we study the split equality fixed point problem and propose a new iterative algorithm with a self-adaptive stepsize that does not need the prior information of the operator norms and is calculated easily. The L-Lipschitz and quasi-pseudo-contractive mappings are chosen as the operators in the algorithm since they have a wider range of applications. Moreover, we prove that the sequence generated by the algorithm strongly converges to the solution of the problem. Finally, we check the feasibility and effectiveness of the algorithm by comparing with other algorithms.