Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 483–491 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa A projected fixed point algorithm with Meir-Keeler contraction for pseudocontractive mappings Yonghong Yao a , Naseer Shahzad b,* , Yeong-Cheng Liou c , Li-Jun Zhu d a Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China. b Department of Mathematics, King Abdulaziz University, P. O. B. 80203, Jeddah 21589, Saudi Arabia. c Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan and Center for General Education, Kaohsiung Medical University, Kaohsiung 807, Taiwan. d School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China. Communicated by Y. J. Cho Abstract In this paper, we introduce a projected algorithm with Meir-Keeler contraction for finding the fixed points of the pseudo- contractive mappings. We prove that the presented algorithm converges strongly to the fixed point of the pseudocontractive mapping in Hilbert spaces. c 2017 All rights reserved. Keywords: Projected algorithm, pseudocontractive mapping, fixed point. 2010 MSC: 47H05, 47H10, 47H17. 1. Introduction In this paper, we assume that H is a real Hilbert space with inner 〈·, ·〉 and norm ‖·‖ and C ⊂ H is a nonempty closed convex set. Recall that a mapping T : C → C is said to be pseudocontractive, if 〈Tu - Tu † , u - u † 〉  ‖u - u † ‖ 2 , ∀u, u † ∈ C. (1.1) It is clear that (1.1) is equivalent to ‖Tu - Tu † ‖ 2  ‖u - u † ‖ 2 + ‖(I - T )u -(I - T )u † ‖ 2 , ∀u, u † ∈ C. (1.2) We use Fix(T ) to denote the set of fixed points of T . Recall also that a mapping T : C → C is said to be L-Lipschitzian, if ‖Tu - Tu † ‖  L‖u - u † ‖, ∀u, u † ∈ C, * Corresponding author Email addresses: yaoyonghong@aliyun.com (Yonghong Yao), nshahzad@kau.edu.sa (Naseer Shahzad), simplex_liou@hotmail.com (Yeong-Cheng Liou), zhulijun1995@sohu.com (Li-Jun Zhu) doi:10.22436/jnsa.010.02.13 Received 2016-04-06