ABSTRACT
In this paper, the concept of weak convex set-valued mapping is introduced and various conditions for a set-valued mapping to be weak convex are given. Then, existence theorems for the Stampacchia variational inequality problem are established, when the involved mapping is weak convex.
Acknowledgments
The author would like to express his gratitude to Professor Nicolas Hadjisavvas for discussions on the present paper and constant encouragement. He wish also to thank the anonymous referee for the careful review and valuable comments, which helped improve the paper.
Disclosure statement
No potential conflict of interest was reported by the author.