IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i12p1189-d293964.html
   My bibliography  Save this article

Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators

Author

Listed:
  • Yonghong Yao

    (School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
    The Key Laboratory of Intelligent Information and Big Data Processing of NingXia Province, North Minzu University, Yinchuan 750021, 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, Bucharest 050711, Romania
    Department of Mathematics and Informatics, University “Politehnica” of Bucharest, Bucharest 060042, Romania)

  • Jen-Chih Yao

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

Abstract

In this paper, we are interested in the pseudomonotone variational inequalities and fixed point problem of pseudocontractive operators in Hilbert spaces. An iterative algorithm has been constructed for finding a common solution of the pseudomonotone variational inequalities and fixed point of pseudocontractive operators. Strong convergence analysis of the proposed procedure is given. Several related corollaries are included.

Suggested Citation

  • Yonghong Yao & Mihai Postolache & Jen-Chih Yao, 2019. "Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1189-:d:293964
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/12/1189/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/12/1189/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. P. E. Maingé & M. L. Gobinddass, 2016. "Convergence of One-Step Projected Gradient Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 146-168, October.
    2. Dang Hieu & Pham Ky Anh & Le Dung Muu, 2019. "Modified extragradient-like algorithms with new stepsizes for variational inequalities," Computational Optimization and Applications, Springer, vol. 73(3), pages 913-932, July.
    3. J. Bello Cruz & A. Iusem, 2010. "Convergence of direct methods for paramonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 46(2), pages 247-263, June.
    4. Jun Yang & Hongwei Liu, 2018. "A Modified Projected Gradient Method for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 197-211, October.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yonghong Yao & Naseer Shahzad & Jen-Chih Yao, 2020. "Projected Subgradient Algorithms for Pseudomonotone Equilibrium Problems and Fixed Points of Pseudocontractive Operators," Mathematics, MDPI, vol. 8(4), pages 1-15, March.
    2. Maryam Gharamah Alshehri & Faizan Ahmad Khan & Faeem Ali, 2022. "An Iterative Algorithm to Approximate Fixed Points of Non-Linear Operators with an Application," Mathematics, MDPI, vol. 10(7), pages 1-16, April.
    3. Jun Yang & Hongwei Liu, 2020. "A self-adaptive method for pseudomonotone equilibrium problems and variational inequalities," Computational Optimization and Applications, Springer, vol. 75(2), pages 423-440, March.
    4. Hasanen A. Hammad & Habib ur Rehman & Manuel De la Sen, 2022. "A New Four-Step Iterative Procedure for Approximating Fixed Points with Application to 2D Volterra Integral Equations," Mathematics, MDPI, vol. 10(22), pages 1-26, November.
    5. Trinh Ngoc Hai, 2020. "Two modified extragradient algorithms for solving variational inequalities," Journal of Global Optimization, Springer, vol. 78(1), pages 91-106, September.
    6. Boţ, R.I. & Csetnek, E.R. & Vuong, P.T., 2020. "The forward–backward–forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces," European Journal of Operational Research, Elsevier, vol. 287(1), pages 49-60.
    7. J. Y. Bello Cruz & R. Díaz Millán, 2014. "A Direct Splitting Method for Nonsmooth Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 728-737, June.
    8. Pham Ky Anh & Trinh Ngoc Hai, 2021. "Dynamical system for solving bilevel variational inequalities," Journal of Global Optimization, Springer, vol. 80(4), pages 945-963, August.
    9. Chanchal Garodia & Afrah A. N. Abdou & Izhar Uddin, 2021. "A New Modified Fixed-Point Iteration Process," Mathematics, MDPI, vol. 9(23), pages 1-10, December.
    10. Javid Ali & Faeem Ali & Puneet Kumar, 2019. "Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
    11. Gdawiec, Krzysztof & Kotarski, Wiesław, 2017. "Polynomiography for the polynomial infinity norm via Kalantari’s formula and nonstandard iterations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 17-30.
    12. Yuanheng Wang & Mingyue Yuan & Bingnan Jiang, 2021. "Multi-Step Inertial Hybrid and Shrinking Tseng’s Algorithm with Meir–Keeler Contractions for Variational Inclusion Problems," Mathematics, MDPI, vol. 9(13), pages 1-13, July.
    13. 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.
    14. Bello Cruz, J.Y. & Iusem, A.N., 2015. "Full convergence of an approximate projection method for nonsmooth variational inequalities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 114(C), pages 2-13.
    15. Pham Ky Anh & Trinh Ngoc Hai, 2019. "Novel self-adaptive algorithms for non-Lipschitz equilibrium problems with applications," Journal of Global Optimization, Springer, vol. 73(3), pages 637-657, March.
    16. Hongwei Liu & Jun Yang, 2020. "Weak convergence of iterative methods for solving quasimonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 77(2), pages 491-508, November.
    17. Alfredo N. Iusem & Alejandro Jofré & Philip Thompson, 2019. "Incremental Constraint Projection Methods for Monotone Stochastic Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 236-263, February.
    18. Zhongming Wu & Min Li, 2019. "General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 73(1), pages 129-158, May.
    19. Andreea Bejenaru & Mihai Postolache, 2022. "New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process," Mathematics, MDPI, vol. 10(19), pages 1-16, October.
    20. J. Y. Bello Cruz & R. Díaz Millán, 2016. "A relaxed-projection splitting algorithm for variational inequalities in Hilbert spaces," Journal of Global Optimization, Springer, vol. 65(3), pages 597-614, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1189-:d:293964. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.