Taiwanese Journal of Mathematics

ON THE CONVERGENCE ANALYSIS OF THE ITERATIVE METHOD WITH ERRORS FOR GENERAL MIXED QUASIVARIATIONAL INEQUALITIES IN HILBERT SPACES

Lu-Chuan Zeng and Jen-Chih Yao

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Abstract

The purpose of this paper is to investigate the iterative methods for a class of general mixed quasivariational inequalities in a Hilbert space. Utilizing the alternative equivalent formulation between general mixed quasivariational inequalities and implicit fixed-point problems, we suggest and analyze a new modified self-adaptive resolvent method with errors for solving this class of general mixed quasivariational inequalities in conjunction with a technique updating the solution. Moreover, we give the convergence analysis of this method in a Hilbert space. Since this class of general mixed quasivariational inequalities includes a number of known classes of variational inequalities as special cases, our results are more general than some earlier and recent ones in the literature.

Article information

Source
Taiwanese J. Math., Volume 10, Number 4 (2006), 949-961.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500403886

Digital Object Identifier
doi:10.11650/twjm/1500403886

Mathematical Reviews number (MathSciNet)
MR2229634

Zentralblatt MATH identifier
1354.49020

Subjects
Primary: 49J30: Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Keywords
mixed quasivariational inequalities fixed points iterative methods

Citation

Zeng, Lu-Chuan; Yao, Jen-Chih. ON THE CONVERGENCE ANALYSIS OF THE ITERATIVE METHOD WITH ERRORS FOR GENERAL MIXED QUASIVARIATIONAL INEQUALITIES IN HILBERT SPACES. Taiwanese J. Math. 10 (2006), no. 4, 949--961. doi:10.11650/twjm/1500403886. https://projecteuclid.org/euclid.twjm/1500403886


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