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Convergence of an iterative algorithm for systems of generalized variational inequalities

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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.

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.

참고문헌 (7)

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

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