Korean J. Math.  Vol 21, No 3 (2013)  pp.213-222
DOI: https://doi.org/10.11568/kjm.2013.21.3.213

Convergence of an iterative algorithm for systems of generalized variational inequalities

Jae Ug Jeong

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. 


Subject classification

49J30; 90C33

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References


L. C. Ceng, C. Y. Wang and J. C. Yao, Strong convergence theorems by a relatively extragradidient method for a general system of variational inequalities, Math. Meth. Oper. Res. 67(2008), 375-390. (Google Scholar)

Z. Huang and M. A. Noor, An explicit projection method for a system of nonlinear variational inequalities with relaxed (gamma,r)-cocoercive mappings, Appl. Math. Comput. 190(2007), 356-361. (Google Scholar)

G. M. Korpelevich, An extragradient method for finding saddle point and for other problem, Ekon Mate Metody 12(1976), 747-756. (Google Scholar)

S. Reich, Asymptotic behavior of contractions in Banach spaces, J. Math. Anal. Appl. 44(1973), 57-70. (Google Scholar)

R. U. Verma, On a new system of nonlinear variational inequalities and associated iterative algorithms, Math. Sci. Res, Hot-line 3(1999), 65-68. (Google Scholar)

X. L. Weng, Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc. 113(1991), 727-731. (Google Scholar)

H. K. Xu, Inequalities in Banch spaces with applications, Nonlinear Anal. 16(1991), 1127-1138. (Google Scholar)

L. C. Ceng, C. Y. Wang and J. C. Yao, Strong convergence theorems by a relatively extragradidient method for a general system of variational inequalities, Math. Meth. Oper. Res. 67(2008), 375-390. (Google Scholar)


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