IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v283y2016icp168-180.html
   My bibliography  Save this article

Generalized viscosity approximation methods for mixed equilibrium problems and fixed point problems

Author

Listed:
  • Jeong, Jae Ug

Abstract

In this paper, we present a new iterative method based on the hybrid viscosity approximation method and the hybrid steepest-descent method for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of common fixed points of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently.

Suggested Citation

  • Jeong, Jae Ug, 2016. "Generalized viscosity approximation methods for mixed equilibrium problems and fixed point problems," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 168-180.
    • Handle: RePEc:eee:apmaco:v:283:y:2016:i:c:p:168-180
    DOI: 10.1016/j.amc.2015.12.044
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315300321
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.12.044?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. H. K. Xu & T. H. Kim, 2003. "Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 185-201, October.
    2. Haiyun Zhou & Peiyuan Wang, 2014. "A Simpler Explicit Iterative Algorithm for a Class of Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 716-727, June.
    3. H.K. Xu, 2003. "An Iterative Approach to Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 659-678, March.
    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. L. C. Zeng & N. C. Wong & J. C. Yao, 2007. "Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 51-69, January.
    2. S. Saeidi & D. S. Kim, 2014. "Combination of the Hybrid Steepest-Descent Method and the Viscosity Approximation," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 911-930, March.
    3. Haiyun Zhou & Peiyuan Wang, 2014. "A Simpler Explicit Iterative Algorithm for a Class of Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 716-727, June.
    4. Nguyen Buong & Lam Thuy Duong, 2011. "An Explicit Iterative Algorithm for a Class of Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 513-524, December.
    5. Kanikar Muangchoo & Poom Kumam & Yeol Je Cho & Sompong Dhompongsa & Sakulbuth Ekvittayaniphon, 2019. "Approximating Fixed Points of Bregman Generalized α -Nonexpansive Mappings," Mathematics, MDPI, vol. 7(8), pages 1-28, August.
    6. Rattanaporn Wangkeeree & Rabian Wangkeeree, 2013. "The general iterative methods for nonexpansive semigroups in Banach spaces," Journal of Global Optimization, Springer, vol. 55(2), pages 417-436, February.
    7. L. C. Ceng & S. Schaible & J. C. Yao, 2008. "Implicit Iteration Scheme with Perturbed Mapping for Equilibrium Problems and Fixed Point Problems of Finitely Many Nonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 403-418, November.
    8. Sitthithakerngkiet, Kanokwan & Deepho, Jitsupa & Kumam, Poom, 2015. "A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 986-1001.
    9. Shengquan Weng & Dingping Wu, 2018. "Convergence Theorems of Modified Proximal Algorithms for Asymptotical Quasi-nonexpansive Mappings in CAT(0) Spaces," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(2), pages 66-76, April.
    10. Mohammad Eslamian & Ali Abkar, 2014. "Viscosity iterative scheme for generalized mixed equilibrium problems and nonexpansive semigroups," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 554-570, July.
    11. F. Cianciaruso & G. Marino & L. Muglia, 2010. "Iterative Methods for Equilibrium and Fixed Point Problems for Nonexpansive Semigroups in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 491-509, August.
    12. Atid Kangtunyakarn, 2013. "A new iterative scheme for fixed point problems of infinite family of κ i -pseudo contractive mappings, equilibrium problem, variational inequality problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1543-1562, August.
    13. Lu-Chuan Ceng & Mihai Postolache & Ching-Feng Wen & Yonghong Yao, 2019. "Variational Inequalities Approaches to Minimization Problems with Constraints of Generalized Mixed Equilibria and Variational Inclusions," Mathematics, MDPI, vol. 7(3), pages 1-20, March.
    14. Wachirapong Jirakitpuwapat & Poom Kumam & Yeol Je Cho & Kanokwan Sitthithakerngkiet, 2019. "A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing," Mathematics, MDPI, vol. 7(3), pages 1-20, February.
    15. Eric U. Ofoedu, 2013. "A General Approximation Scheme for Solutions of Various Problems in Fixed Point Theory," International Journal of Analysis, Hindawi, vol. 2013, pages 1-18, January.
    16. Lu-Chuan Ceng & Yekini Shehu & Jen-Chih Yao, 2022. "Modified Mann Subgradient-like Extragradient Rules for Variational Inequalities and Common Fixed Points Involving Asymptotically Nonexpansive Mappings," Mathematics, MDPI, vol. 10(5), pages 1-20, February.
    17. Rapeepan Kraikaew & Satit Saejung, 2012. "On Maingé’s Approach for Hierarchical Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 71-87, July.
    18. Uthai Kamraksa & Rabian Wangkeeree, 2011. "Generalized equilibrium problems and fixed point problems for nonexpansive semigroups in Hilbert spaces," Journal of Global Optimization, Springer, vol. 51(4), pages 689-714, December.
    19. Lu-Chuan Ceng & Adrian Petruşel & Jen-Chih Yao, 2019. "On Mann Viscosity Subgradient Extragradient Algorithms for Fixed Point Problems of Finitely Many Strict Pseudocontractions and Variational Inequalities," Mathematics, MDPI, vol. 7(10), pages 1-14, October.
    20. Yun-Ling Cui & Lu-Chuan Ceng & Fang-Fei Zhang & Cong-Shan Wang & Jian-Ye Li & Hui-Ying Hu & Long He, 2022. "Modified Mann-Type Subgradient Extragradient Rules for Variational Inequalities and Common Fixed Points Implicating Countably Many Nonexpansive Operators," Mathematics, MDPI, vol. 10(11), pages 1-26, June.

    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:eee:apmaco:v:283:y:2016:i:c:p:168-180. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.