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Strong Convergence Theorems for Variational Inequalities and Common Fixed-Point Problems Using Relaxed Mann Implicit Iteration Methods

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  • Lu-Chuan Ceng

    (Department of Mathematics, Shanghai Normal University, Shanghai 201416, China)

  • Meijuan Shang

    (College of Science, Shijiazhuang University, Shijiazhuang 266100, China)

Abstract

Mann-like iteration methods are significant to deal with convex feasibility problems in Banach spaces. We focus on a relaxed Mann implicit iteration method to solve a general system of accretive variational inequalities with an asymptotically nonexpansive mapping in the intermediate sense and a countable family of uniformly Lipschitzian pseudocontractive mappings. More convergence theorems are proved under some suitable weak condition in both 2-uniformly smooth and uniformly convex Banach spaces.

Suggested Citation

  • Lu-Chuan Ceng & Meijuan Shang, 2019. "Strong Convergence Theorems for Variational Inequalities and Common Fixed-Point Problems Using Relaxed Mann Implicit Iteration Methods," Mathematics, MDPI, vol. 7(5), pages 1-16, May.
  • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:424-:d:230383
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    References listed on IDEAS

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    1. Lu-Chuan Ceng & Chang-yu Wang & Jen-Chih Yao, 2008. "Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 375-390, June.
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