Modified Mann Subgradient-like Extragradient Rules for Variational Inequalities and Common Fixed Points Involving Asymptotically Nonexpansive Mappings

Lu-Chuan Ceng, Yekini Shehu and Jen-Chih Yao
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Lu-Chuan Ceng: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Yekini Shehu: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
Jen-Chih Yao: Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Mathematics, 2022, vol. 10, issue 5, 1-20

Abstract: In a real Hilbert space, we aim to investigate two modified Mann subgradient-like methods to find a solution to pseudo-monotone variational inequalities, which is also a common fixed point of a finite family of nonexpansive mappings and an asymptotically nonexpansive mapping. We obtain strong convergence results for the sequences constructed by these proposed rules. We give some examples to illustrate our analysis.

Keywords: modified Mann subgradient-like extragradient rule; pseudo-monotone variational inequality; common fixed point problem; asymptotically nonexpansive mapping; line-search process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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