Predictor-Corrector Methods for Generalized General Multivalued Mixed Quasi Variational Inequalities

Volume 4, Issue 2, 2003

Article 38

PREDICTOR-CORRECTOR METHODS FOR GENERALIZED GENERAL MULTIVALUED MIXED QUASI VARIATIONAL INEQUALITIES

CHAO FENG SHI, SAN YANG LIU AND LIAN JUN LI

DEPARTMENT OF APPLIED MATHEMATICS,
XIDIAN UNIVERSITY,
XI'AN, 710071, P.R. CHINA
E-Mail: Shichf@163.com

Received 04 April, 2003; Accepted 01 May, 2003.
Communicated by: S.S. Dragomir

ABSTRACT. In this paper, a class of generalized general mixed quasi variational inequalities is introduced and studied. We prove the existence of the solution of the auxiliary problem for the generalized general mixed quasi variational inequalities, suggest a predictor-corrector method for solving the generalized general mixed quasi variational inequalities by using the auxiliary principle technique. If the bi-function involving the mixed quasi variational inequalities is skew-symmetric, then it is shown that the convergence of the new method requires the partially relaxed strong monotonicity property of the operator, which is a weak condition than cocoercivity. Our results can be viewed as an important extension of the previously known results for variational inequalities.

Key words:
Variational inequalities, Auxiliary principle, Predictor-corrector method, Convergence.

2000 Mathematics Subject Classification:
11N05, 11N37.

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