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Solving System of Mixed Variational Inclusions Involving Generalized Cayley Operator and Generalized Yosida Approximation Operator with Error Terms in q -Uniformly Smooth Space

Author

Listed:
  • Rais Ahmad

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Mohd Ishtyak

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Arvind Kumar Rajpoot

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Yuanheng Wang

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China)

Abstract

In this paper, we solve a system of mixed variational inclusions involving a generalized Cayley operator and the generalized Yosida approximation operator. An iterative algorithm is suggested to discuss the convergence analysis. We have shown that our system admits a unique solution by using the properties of q -uniformly smooth Banach space, and we discuss the convergence criteria for sequences generated by iterative algorithm. Two examples are constructed, and an application is provided.

Suggested Citation

  • Rais Ahmad & Mohd Ishtyak & Arvind Kumar Rajpoot & Yuanheng Wang, 2022. "Solving System of Mixed Variational Inclusions Involving Generalized Cayley Operator and Generalized Yosida Approximation Operator with Error Terms in q -Uniformly Smooth Space," Mathematics, MDPI, vol. 10(21), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4131-:d:964146
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    References listed on IDEAS

    as
    1. Rais Ahmad & Iqbal Ahmad & Zahoor Ahmad Rather & Yuanheng Wang & Sun Young Cho, 2021. "Generalized Complementarity Problem with Three Classes of Generalized Variational Inequalities Involving ⊕ Operation," Journal of Mathematics, Hindawi, vol. 2021, pages 1-10, January.
    2. Javid Iqbal & Arvind Kumar Rajpoot & Monirul Islam & Rais Ahmad & Yuanheng Wang, 2022. "System of Generalized Variational Inclusions Involving Cayley Operators and XOR-Operation in q -Uniformly Smooth Banach Spaces," Mathematics, MDPI, vol. 10(16), pages 1-13, August.
    3. 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.
    4. Saeed Althubiti & Abdelaziz Mennouni, 2022. "A Novel Projection Method for Cauchy-Type Systems of Singular Integro-Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-11, July.
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