Summary: Journal of Inequalities in Pure and
Volume 4, Issue 1, Article 6, 2003
RELATIVELY B-PSEUDOMONOTONE VARIATIONAL INEQUALITIES OVER
PRODUCT OF SETS
QAMRUL HASAN ANSARI AND ZUBAIR KHAN
DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY
ALIGARH 202 002, INDIA.
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 pseudomono-
tonicity 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 and phrases: Variational inequalities, System of variational inequalities, Relatively B-pseudomonotone maps, Co-