Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

CONVERGENCE AND STABILITY OF THREE-STEP ITERATIVE SCHEME WITH ERRORS FOR COMPLETELY GENERALIZED STRONGLY NONLINEAR QUASIVARIATIONAL INEQUALITIES

  • ZHANG FENGRONG (College of Information Science and Engineering, Dalian Institute of Light Industry, Dalian) ;
  • GAO HAIYAN (Department of Mathematics, Liaoning Normal University, Dalian) ;
  • LIU ZEQING (Department of Mathematics, Liaoning Normal University) ;
  • KANG SHIN MIN (Department of Mathemtaics and Research Institute of Natural Science, Gyeongsang National University)
  • Published : 2006.01.01

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Abstract

In this paper, we introduce a new class of completely generalized strongly nonlinear quasivariational inequalities and establish its equivalence with a class of fixed point problems by using the resolvent operator technique. Utilizing this equivalence, we develop a three-step iterative scheme with errors, obtain a few existence theorems of solutions for the completely generalized non-linear strongly quasivariational inequality involving relaxed monotone, relaxed Lipschitz, strongly monotone and generalized pseudocontractive mappings and prove some convergence and stability results of the sequence generated by the three-step iterative scheme with errors. Our results include several previously known results as special cases.

Keywords