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

Lu-Chuan Ceng and Meijuan Shang
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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

Mathematics, 2019, vol. 7, issue 5, 1-16

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.

Keywords: relaxed Mann implicit iteration; general variational inequalities; countable many uniformly Lipschitzian pseudocontractions; asymptotically nonexpansive mapping in the intermediate sense; banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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