A strong convergence algorithm for a fixed point constrained split null point problem

TLDR: In this article, a self-adaptive step-size method for finding a common solution of a split feasibility problem and a fixed point problem in real Hilbert spaces is proposed. But the authors do not consider the operator norm in the proposed method.

Abstract: In this paper, we introduce a new algorithm with self adaptive step-size for finding a common solution of a split feasibility problem and a fixed point problem in real Hilbert spaces. Motivated by the self adaptive step-size method, we incorporate the self adaptive step-size to overcome the difficulty of having to compute the operator norm in the proposed method. Under standard and mild assumption on the control sequences, we establish the strong convergence of the algorithm, obtain a common element in the solution set of a split feasibility problem for sum of two monotone operators and fixed point problem of a demimetric mapping. Numerical examples are presented to illustrate the performance and the behavior of our method. Our result extends, improves and unifies other results in the literature.