IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n513678.html

Strong and Weak Convergence Criteria of Composite Iterative Algorithms for Systems of Generalized Equilibria

Author

Listed:
  • Lu-Chuan Ceng
  • Cheng-Wen Liao
  • Chin-Tzong Pang
  • Ching-Feng Wen
  • Zhao-Rong Kong

Abstract

We first introduce and analyze one iterative algorithm by using the composite shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: a generalized mixed equilibrium problem, finitely many variational inequalities, and the common fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense and infinitely many nonexpansive mappings in a real Hilbert space. We prove a strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions. Our results improve and extend the corresponding results in the earlier and recent literature.

Suggested Citation

  • Lu-Chuan Ceng & Cheng-Wen Liao & Chin-Tzong Pang & Ching-Feng Wen & Zhao-Rong Kong, 2014. "Strong and Weak Convergence Criteria of Composite Iterative Algorithms for Systems of Generalized Equilibria," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:513678
    DOI: 10.1155/2014/513678
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/513678
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/513678?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
    ---><---

    References listed on IDEAS

    as
    1. Eberhard Zeidler, 1985. "Nonlinear Functional Analysis and its Applications," Springer Books, Springer, number 978-1-4612-5020-3, 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. Lu-Chuan Ceng & Ching-Feng Wen, 2012. "Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed‐Point Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Qian-Fen Gong & Dao-Jun Wen, 2014. "Further Investigation on the Relaxed Hybrid Steepest‐Descent Methods for Variational Inequalities with k‐Strict Pseudocontractions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Lu-Chuan Ceng & Juei-Ling Ho, 2014. "Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. A. E. Al-Mazrooei & A. Latif & J. C. Yao, 2014. "Solving Generalized Mixed Equilibria, Variational Inequalities, and Constrained Convex Minimization," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Dandan Yang & Chuanzhi Bai, 2014. "Three Weak Solutions for Nonlocal Fractional Laplacian Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. Shapour Heidarkhani, 2012. "Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One‐Dimensional (p1, …, pn)‐Laplacian Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Lu-Chuan Ceng & Suliman Al-Homidan, 2014. "Algorithms of Common Solutions for Generalized Mixed Equilibria, Variational Inclusions, and Constrained Convex Minimization," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. Lu-Chuan Ceng & Cheng-Wen Liao & Chin-Tzong Pang & Ching-Feng Wen, 2014. "Triple Hierarchical Variational Inequalities with Constraints of Mixed Equilibria, Variational Inequalities, Convex Minimization, and Hierarchical Fixed Point Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    9. Lu-Chuan Ceng & Adrian Petrusel & Mu-Ming Wong & Jen-Chih Yao, 2014. "Hybrid Algorithms for Solving Variational Inequalities, Variational Inclusions, Mixed Equilibria, and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    10. Zhao-Rong Kong & Lu-Chuan Ceng & Ching-Feng Wen, 2012. "Some Modified Extragradient Methods for Solving Split Feasibility and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    11. Qing Miao, 2016. "Multiple Solutions for Nonlinear Navier Boundary Systems Involving (p1(x), …, pn(x))‐Biharmonic Problem," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    12. Li, Dingshi & Pu, Zhe, 2026. "Discretization of invariant measures for stochastic lattice dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 473-493.
    13. Lu-Chuan Ceng & Ching-Feng Wen, 2012. "Well‐Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    14. Lu-Chuan Ceng & Chi-Ming Chen & Chin-Tzong Pang, 2014. "Hybrid Extragradient‐Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlaaa:v:2014:y:2014:i:1:n:513678. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.