Hybrid Iterative Approximation Method for a Fixed Point of Nonexpansive Mapping and Equilibrium Problem

Article Preview

Abstract:

In this paper, a iterative method for approximating equilibrium problem and a fixed point of nonexpansive mappings was introduced in Hilbert spaces. And a strong convergence theorems of the iteration scheme was established. The results improve and extend the corresponding results of many others.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

789-792

Citation:

Online since:

June 2014

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2014 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] S. Takahashi, W. Takahashi. Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces[J]. Math. Anal. Appl. 2007, 331: 506~515.

DOI: 10.1016/j.jmaa.2006.08.036

Google Scholar

[2] L.C. Ceng, C.Y. Wang, J.C. Yao. Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities[J]. Math. Methods Oper. Res. 2008, 67: 375~390.

DOI: 10.1007/s00186-007-0207-4

Google Scholar

[3] Combettes P L, Hirstoaga S A. Equilibrium problem progamming in Hilbert spaces[J]. Nonlinear Convex Anal. 2005, 06: 117~136.

Google Scholar

[4] T. Suzuki. Strong convergence of Krasnoselslskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochne integrals[J]. Math. Anal. Appl. 2005, 305: 227~239.

DOI: 10.1016/j.jmaa.2004.11.017

Google Scholar

[5] H.K. Xu. Iterative algorithms for nonlinear operators[J]. London Math. Soc. 2002, 66: 240~256.

Google Scholar