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A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces

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  • Yuanheng Wang

    (College of Mathematics and Computer Science, with College of Xingzhi, Zhejiang Normal University, 268 Yingbin Road, Jinhua 321004, Zhejiang, China)

  • Cancan Li

    (College of Mathematics and Computer Science, with College of Xingzhi, Zhejiang Normal University, 268 Yingbin Road, Jinhua 321004, Zhejiang, China
    These authors contributed equally to this work.)

  • Lirong Lu

    (College of Mathematics and Computer Science, with College of Xingzhi, Zhejiang Normal University, 268 Yingbin Road, Jinhua 321004, Zhejiang, China
    These authors contributed equally to this work.)

Abstract

We study a new algorithm for the common solutions of a generalized variational inequality system and the fixed points of an asymptotically non-expansive mapping in Banach spaces. Under some specific assumptions imposed on the control parameters, some strong convergence theorems for the sequence generated by our new viscosity iterative scheme to approximate their common solutions are proved. As an application of our main results, we solve the standard constrained convex optimization problem. The results here generalize and improve some other authors’ recently corresponding results.

Suggested Citation

  • Yuanheng Wang & Cancan Li & Lirong Lu, 2020. "A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces," Mathematics, MDPI, vol. 8(11), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1944-:d:439634
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    References listed on IDEAS

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    1. Chanjuan Pan & Yuanheng Wang, 2019. "Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces," Mathematics, MDPI, vol. 7(5), pages 1-13, April.
    2. 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.
    3. Zhenhua He & Wei-Shih Du, 2012. "Viscosity Iterative Schemes for Finding Split Common Solutions of Variational Inequalities and Fixed Point Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, November.
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    1. Wei-Shih Du & Chung-Chuan Chen & Marko Kostić & Bessem Samet, 2023. "Preface to the Special Issue “Fixed Point Theory and Dynamical Systems with Applications”," Mathematics, MDPI, vol. 11(13), pages 1-2, June.

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