Existence result and error bounds for a new class of inverse mixed quasi-variational inequalities

Abstract

Abstract In this paper, a new class of inverse mixed quasi-variational inequalities (IMQVI) is introduced and studied in Hilbert spaces. This type of inequalities includes many quasi-variational inequalities and inverse variational inequalities as its special cases. We first prove some properties of generalized f-projection operators in Hilbert spaces. Then we use these properties to obtain the existence and uniqueness result. Moreover, error bounds for IMQVI in terms of the residual function are also established. The results presented in this paper are new and improve some results in the recent literature.

Keywords

• mixed variational inequality
• inverse mixed quasi-variational inequality
• generalized f-projection operator
• error bound
• residual function