Relatively B-Pseudomonotone Variational Inequalities Over Product of Sets

Volume 4, Issue 1, 2003

Article 6

B-PSEUDOMONOTONE VARIATIONAL INEQUALITIES OVER PRODUCT OF SETS

DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY
ALIGARH 202 002, INDIA.
E-Mail: qhansari@sancharnet.in

Received 09 October, 2002; Accepted 14 November, 2002.
Communicated by: Th.M. Rassias

ABSTRACT. In this paper, we consider variational inequality problem over the product of sets which is equivalent to the problem of system of variational inequalities. These two problems are studied for single valued maps as well as for multivalued maps. New concept of pseudomonotonicity in the sense of Brézis is introduced to prove the existence of a solution of our problems. As an application of our results, the existence of a coincidence point of two families of operators is also established.

Key words:
Variational inequalities, System of variational inequalities, Relatively B-pseudomonotone maps, Coincidence point.

2000 Mathematics Subject Classification:
49Jxx, 47Hxx.

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