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An algorithm for finding common solutions of various problems in nonlinear operator theory
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  • 作者：Eric U Ofoedu (9)
    Jonathan N Odumegwu (9)
    Habtu Zegeye (10)
    Naseer Shahzad (11)
  • 关键词：classical equilibrium problem ; generalized mixed equilibrium problem ; 畏 ; inverse strongly monotone mapping ; maximal monotone operator ; nonexpansive mappings ; real Hilbert space ; pseudocontractive mappings ; variational inequality problem
  • 刊名：Fixed Point Theory and Applications
  • 出版年：2014
  • 出版时间：December 2014
  • 年：2014
  • 卷：2014
  • 期：1
  • 全文大小：
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  • 作者单位：Eric U Ofoedu (9)
    Jonathan N Odumegwu (9)
    Habtu Zegeye (10)
    Naseer Shahzad (11)

    9. Department of Mathematics, Nnamdi Azikiwe University, P.M.B. 5025, Awka, Anambra State, Nigeria
    10. Bahir Dar University, P.O. Box 859, Bahir Dar, Ethiopia
    11. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
  • ISSN：1687-1812
文摘
In this paper, it is our aim to prove strong convergence of a new iterative algorithm to a common element of the set of solutions of a finite family of classical equilibrium problems; a common set of zeros of a finite family of inverse strongly monotone operators; the set of common fixed points of a finite family of quasi-nonexpansive mappings; and the set of common fixed points of a finite family of continuous pseudocontractive mappings in Hilbert spaces on assumption that the intersection of the aforementioned sets is not empty. Moreover, the common element is shown to be the metric projection of the initial guess on the intersection of these sets. MSC: 47H06, 47H09, 47J05, 47J25.

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