Convergence and stability of three-step iterative scheme with errors for completely generalized strongly nonlinear quasivariational inequalities

被引：1

作者：

Zhang F. ^{[1
,2
]}

Gao H. ^{[3
]}

Liu Z. ^{[4
]}

Kang S.M. ^{[5
,6
]}

机构：

[1] College of Information Science and Engineering, Dalian Institute of Light Industry, Dalian

[2] North East University, Shenyang

[3] Department of Mathematics, Liaoning Normal University, Dalian

[4] Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029

[5] Research Institute of Natural Science, Gyeongsang National University

[6] Department of Mathematics, Research Institute of Natural Science, Gyeongsang National University

来源：

Journal of Applied Mathematics and Computing | 2006年 / 20卷 / 1-2期

关键词：

Completely generalized strongly nonlinear quasivariational inequality; Generalized pseudocontractive mapping; Maximal monotone mapping; Relaxed lipschitz mapping; Relaxed monotone mapping; Strongly monotone mapping; Three-step iterative scheme with errors;

D O I：

10.1007/BF02831953

中图分类号：

学科分类号：

摘要：

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. © 2006 Korean Society or Computational & Applied Mathematics and Korean SIGCAM.

引用

页码：465 / 478

页数：13

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