[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2013.21.3.213

CONVERGENCE OF AN ITERATIVE ALGORITHM FOR SYSTEMS OF GENERALIZED VARIATIONAL INEQUALITIES

Jeong, Jae Ug (Department of Mathematics Dongeui University)

Publication Information

Korean Journal of Mathematics / v.21, no.3, 2013 , pp. 213-222 More about this Journal

Abstract

In this paper, we introduce and consider a new system of generalized variational inequalities involving five different operators. Using the sunny nonexpansive retraction technique we suggest and analyze some new explicit iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities.

Keywords

Accretive mapping; Relaxed cocoercive mapping; Convergence; Variational inequality; Sunny nonexpansive retraction;

Citations & Related Records

Reference

1	L. C. Ceng, C. Y. Wang and J. C. Yao, Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Meth. Oper. Res. 67(2008), 375-390. DOI ScienceOn
2	Z. Huang and M. A. Noor, An explicit projection method for a system of nonlinear variational inequalities with different ( ${\gamma}$ , r)-cocoercive mappings, Appl. Math. Comput. 190(2007), 356-361. DOI ScienceOn
3	G. M. Korpelevich, An extragradient method for finding saddle point and for other problem, Ekon Mate Metody 12(1976), 747-756.
4	S. Reich, Asymptotic behavior of contractions in Banach spaces, J. Math. Anal. Appl. 44(1973), 57-70. DOI
5	R. U. Verma, On a new system of nonlinear variational inequalities and associated iterative algorithms, Math. Sci. Res. 3(1999), 65-68.
6	X. L. Weng, Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc. 113(1991), 727-731. DOI ScienceOn
7	H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. 16(1991), 1127-1138. DOI ScienceOn