Iterative Methods for a Generalized Equilibrium Problem and a Nonexpansive Multi-Valued Mapping

被引：2
作者：
Buangern A. [1 ]
Aeimrun A. [1 ]
Cholamjiak W. [1 ]
机构：
[1] School of Science, University of Phayao, Phayao
来源：
Vietnam Journal of Mathematics | 2017年 / 45卷 / 3期
关键词：
Generalized equilibrium problem; Hilbert space; Iteration; Nonexpansive multi-valued mapping; Variational inequality;
D O I：
10.1007/s10013-016-0225-8
中图分类号：
学科分类号：
摘要：
In this paper, we introduce new iterative schemes for approximating common elements of the set of solutions of generalized equilibrium problems and the set of fixed points of nonexpansive multi-valued mappings. We prove some strong convergence theorems of the sequences generated by our iterative process under appropriate additional assumptions in Hilbert spaces. Moreover, we give some numerical results for supporting our main theorem. Our main results improve the corresponding ones obtained in (S. Takahashi, W. Takahashi: Nonlinear Anal. 69: 1025–1033, 2008). © 2016, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.
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页码：477 / 492
页数：15
相关论文
共 40 条
  • [1] Anh P.N., Muu L.D., Nguyen V.H., Strodiot J.J., Using the Banach contraction principle to implement the proximal point method for multivalued monotone variational inequalities, J. Optim. Theory Appl., 124, pp. 285-306, (2005)
  • [2] Aoyama K., Kimura Y., Takahashi W., Maximal monotone operators and maximal monotone functions for equilibrium problems, J. Convex Anal., 15, pp. 395-409, (2008)
  • [3] Aoyama K., Kimura Y., Takahashi W., Toyoda M., Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space, Nonlinear Anal. TMA, 67, pp. 2350-2360, (2007)
  • [4] Assad N.A., Kirk W.A., Fixed point theorems for set-valued mappings of contractive type, Pac. J. Math., 43, pp. 553-562, (1972)
  • [5] Blum E., Oettli W., From optimization and variational inequalities to equilibrium problems, Math. Stud., 63, pp. 123-145, (1994)
  • [6] Ceng L.-C., Ansari Q.H., Yao J.-C., Mann-type steepest-descent and modified hybrid steepest-descent methods for variational inequalities in Banach spaces, Numer. Funct. Anal. Optim., 29, pp. 987-1033, (2008)
  • [7] Ceng L.-C., Yao J.-C., A hybrid iterative scheme for mixed equilibrium problems and fixed point problems, J. Comput. Appl. Math., 214, pp. 186-201, (2008)
  • [8] Cianciaruso F., Marino G., Muglia L., Yao Y., A hybrid projection algorithm for finding solutions of mixed equilibrium problem and variational inequality problem, Fixed Point Theory Appl., 2010, (2010)
  • [9] Combettes P.L., Hirstoaga S.A., Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal., 6, pp. 117-136, (2005)
  • [10] Harker P.T., Pang J.-S., Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications, Math. Program., 48, pp. 161-220, (1990)
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