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An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems

Author

Listed:
  • Yonghong Yao

    (School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China)

  • Mihai Postolache

    (Center for General Education, China Medical University, Taichung 40402, Taiwan
    Romanian Academy, Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, 050711 Bucharest, Romania
    Department of Mathematics and Informatics, University “Politehnica” of Bucharest, 060042 Bucharest, Romania)

  • Jen-Chih Yao

    (Center for General Education, China Medical University, Taichung 40402, Taiwan)

Abstract

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated.

Suggested Citation

  • Yonghong Yao & Mihai Postolache & Jen-Chih Yao, 2019. "An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems," Mathematics, MDPI, vol. 7(1), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:61-:d:195884
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    References listed on IDEAS

    as
    1. Yonghong Yao & Mihai Postolache, 2012. "Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 273-287, October.
    2. Minglu Ye & Yiran He, 2015. "A double projection method for solving variational inequalities without monotonicity," Computational Optimization and Applications, Springer, vol. 60(1), pages 141-150, January.
    3. Thakur, Balwant Singh & Thakur, Dipti & Postolache, Mihai, 2016. "A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 147-155.
    4. Fu-Quan Xia & Nan-Jing Huang, 2011. "A Projection-Proximal Point Algorithm for Solving Generalized Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 98-117, July.
    5. Benar F. Svaiter, 2014. "A Class of Fejér Convergent Algorithms, Approximate Resolvents and the Hybrid Proximal-Extragradient Method," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 133-153, July.
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    Cited by:

    1. María Isabel Berenguer & Manuel Ruiz Galán, 2022. "An Iterative Algorithm for Approximating the Fixed Point of a Contractive Affine Operator," Mathematics, MDPI, vol. 10(7), pages 1-10, March.
    2. Arvind Kumar Rajpoot & Mohd Ishtyak & Rais Ahmad & Yuanheng Wang & Jen-Chih Yao, 2023. "Convergence Analysis for Yosida Variational Inclusion Problem with Its Corresponding Yosida Resolvent Equation Problem through Inertial Extrapolation Scheme," Mathematics, MDPI, vol. 11(3), pages 1-19, February.

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