Some iterative algorithms for Reich-Suzuki nonexpansive mappings and relaxed $(\alpha,k)$-cocoercive mapping with applications to a fixed point and optimization problems

Document Type : Research Paper


1 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

2 DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS)

3 Department of Computer Science and Mathematics, Mountain Top University, Prayer City, Ogun State, Nigeria


In this paper, we propose an iterative method for finding the common element of the set of fixed points of Reich-Suzuki nonexpansive mappings and the set of solutions of the variational inequalities problems in the framework of Hilbert spaces. In addition, we establish convergence results for these proposed iterative methods under some mild conditions. Furthermore, we establish analytically and numerically that our newly proposed iterative method converges to a common element of the set of fixed points of a Reich-Suzuki nonexpansive mapping and the set of solutions of the variational inequalities problems faster compared to some well-known iterative methods in the literature. Finally, we apply our proposed iterative method to approximate the solution of a convex minimization problem. The results obtained in this paper improve, extend and unify some related results in the literature.


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Volume 14, Issue 2
February 2023
Pages 175-193
  • Receive Date: 03 May 2022
  • Revise Date: 17 August 2022
  • Accept Date: 24 August 2022