Journal of applied mathematics & informatics
- Volume 20 Issue 1_2
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- Pages.465-478
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- 2006
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- 2734-1194(pISSN)
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- 2234-8417(eISSN)
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
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
- Completely generalized strongly nonlinear quasivariational inequality;
- three-step iterative scheme with errors;
- maximal monotone mapping;
- relaxed Lipschitz mapping;
- relaxed monotone mapping;
- strongly mono-tone mapping;
- generalized pseudocontractive mapping;
- convergence;
- stability