Some well-posedness equivalent results for a generalized split variational-hemivariational inequality

Abstract

In this paper, we introduce a generalized split variational-hemivariational inequality in Banach space and are devoted to discussing the equivalence of this inequality with its derived inclusion problem and associated problem. Under very mild assumptions, we prove that the three problems contain the same solution. Moreover, we also show the equivalence of the strong and weak well-posedness of these problems. Finally, we give some equivalent conditions for the strong and weak well-posedness.

Keywords:

• Generalized split variational-hemivariational inequality
• well-posedness
• derived inclusion problem
• associated problem

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission [grant number CSTB2022NSCQ-MSX0404], the Science and Technology Research Program of Chongqing Municipal Education Commission [grant number KJQN202001601], and the Research Program of Chongqing University of Education [grant number KY202303B].