Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 3856–3862 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa A regularization algorithm for a splitting feasibility problem in Hilbert spaces Abdul Latif a , Xiaolong Qin b,∗ a Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah-21589, Saudi Arabia. b Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Sichuan, China. Communicated by Y. J. Cho Abstract In this article, we investigate a split feasibility problem via a regularization iterative algorithm. Strong convergence theorems of solutions for the split feasibility are established in the framework of Hilbert spaces. We also apply our main results to the split equality problem. c 2017 All rights reserved. Keywords: Metric projection, monotone operator, nonexpansive mapping, split feasibility problem, variational inequality. 2010 MSC: 47H05, 47H09, 90C33. 1. Introduction In this paper, we always assume that H 1 and H 2 are real Hilbert spaces endowed with inner products and induced norms denoted by 〈·, ·〉 and ‖·‖, respectively, while H refers to as any of these spaces. Let D be a nonempty closed and convex subset of H. Recall that Proj H D is said to be a metric projection from H onto D iff ‖x - Proj H D x‖  ‖x - y‖, ∀x ∈ H, y ∈ D. It is known that 〈x - y, Proj H D x - Proj H D y〉  ‖Proj H D x - Proj H D y‖ 2 , ∀x, y ∈ H. Moreover, Proj H D x is also characterized by the fact P D x ∈ C and 〈x - Proj H D x, y - Proj H D x〉  0, and ‖x - y‖ 2  ‖x - Proj H D x‖ 2 + ‖y - Proj H D x‖ 2 , ∀x ∈ H, y ∈ C. Recall that a mapping M : H → H is said to be contractive iff there exists a constant κ ∈ (0, 1) such that ‖Mx - My‖  κ‖x - y‖, ∀x, y ∈ H. ∗ Corresponding author Email addresses: alatif@kau.edu.sa (Abdul Latif), qxlxajh@163.com (Xiaolong Qin) doi:10.22436/jnsa.010.07.40 Received 2017-05-14