Multivalued Quasi Variational Inequalities in Banach Spaces

Volume 3, Issue 3, 2002

Article 36

MULTIVALUED QUASI VARIATIONAL INEQUALITIES IN BANACH SPACES

MUHAMMAD ASLAM NOOR, ABDELLATIF MOUDAFI AND BENLONG XU

ETISALAT COLLEGE OF ENGINEERING,
SHARJAH, UNITED ARAB EMIRATES
E-Mail: noor@ece.ac.ae

UNIVERSITE ANTILLES GUYANE
GRIMAAG, DEPARTEMENT SCIENTIFIQUE
INTERFACULTAIRES, 97200 SCHELCHER,
MARTINIQUE, FRANCE
E-Mail: noor@ece.ac.ae

DEPARTMENT OF MATHEMATICS,
QUFU NORMAL UNIVERSITY
QUFU SHANDONG, 273165,
PEOPLE'S REPUBLIC OF CHINA.

Received 22 February, 2002; Accepted 22 February, 2002;.
Communicated by: Th. M. Rassias

ABSTRACT. It is established that the multivalued quasi variational inequalities in uniformly smooth Banach spaces are equivalent to the fixed-point problem. We use this equivalence to suggest and analyze some iterative algorithms for quasi variational inequalities with noncompact sets in Banach spaces. Our results are new and represent a significant improvement of the previously known results.

Key words:
Variational inequalities, Banach spaces, Iterative algorithms, Convergence analysis.

2000 Mathematics Subject Classification:
49J40, 90C33.

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