Iterative approximation of a common solution of a split generalized equilibrium problem and a fixed point problem for nonexpansive semigroup

被引：26

作者：

Kazmi K.R. ^{[1
]}

Rizvi S.H. ^{[1
]}

机构：

[1] Department of Mathematics, Aligarh Muslim University, Aligarh

来源：

Mathematical Sciences | 2013年 / 7卷 / 1期

关键词：

47J25; 65J15; 65K15; 90C33; Fixed point problem; Nonexpansive semigroup; Split generalized equilibrium problem;

D O I：

10.1186/2251-7456-7-1

中图分类号：

学科分类号：

摘要：

Purpose: In this paper, we introduce and study an iterative method to approximate a common solution of a split generalized equilibrium problem and a fixed point problem for a nonexpansive semigroup in real Hilbert spaces. Methods: We prove a strong convergence theorem of the iterative algorithm in Hilbert spaces under certain mild conditions. Results: We obtain a strong convergence result for approximating a common solution of a split generalized equilibrium problem and a fixed point problem for a nonexpansive semigroup in real Hilbert spaces, which is a unique solution of a variational inequality problem. Further, we obtain some consequences of our main result. Conclusions: The results presented in this paper are the supplement, extension, and generalization of results in the study of Plubtieng and Punpaeng and that of Cianciaruso et al. The approach of the proof given in this paper is also different. © 2013, Kazmi and Rizvi; licensee Springer.

引用

共 19 条

[1]

Marino G., Xu H.K., A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl, 318, pp. 43-52, (2006)

[2]

Shimizu T., Takahashi W., Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl, 211, pp. 71-83, (1997)

[3]

Chen R., Song Y., Convergence to common fixed point of nonexpansive semigroups, J. Comput. Appl. Math, 200, pp. 566-575, (2007)

[4]

Plubtieng S., Punpaeng R., Fixed point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces, Math. Comput. Model, 48, pp. 279-286, (2008)

[5]

Blum E., Oettli W., From optimization and variational inequalities to equilibrium problems, Math. Stud, 63, pp. 123-145, (1994)

[6]

Cianciaruso F., Marino G., Muglia L., Iterative methods for equilibrium and fixed point problems for nonexpansive semigroups in Hilbert space, J. Optim. Theory Appl, 146, pp. 491-509, (2010)

[7]

Moudafi A., Split monotone variational inclusions, J. Optim. Theory Appl, 150, pp. 275-283, (2011)

[8]

Censor Y., Gibali A., Reich S., Algorithms for the split variational inequality problem, Numer. Algorithm, 59, 2, pp. 301-323, (2012)

[9]

Moudafi A., The split common fixed point problem for demicontractive mappings, Inverse Probl, 26, (2010)

[10]

Byrne C., Censor Y., Gibali A., Reich S., The split common null point problem, J. Nonlinear Convex Anal, 13, 4, pp. 759-775, (2012)

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