Error bounds for mixed set-valued vector inverse quasi-variational inequalities

Abstract

The purpose of this paper is to introduce and study the mixed set-valued vector inverse quasi-variational inequality problems (MSVIQVIPs) and to obtain error bounds for this kind of MSVIQVIP in terms of the residual gap function, the regularized gap function, and the D-gap function. These bounds provide effective estimated distances between an arbitrary feasible point and the solution set of mixed set-valued vector inverse quasi-variational inequality problem. The results presented in the paper improve and generalize some recent results.

An Approximation Theorem and Generic Convergence of Solutions of Inverse Quasivariational Inequality Problems

“…Besides, the convergence consequent on the Euler time-dependent scheme was proved [6] (iv) For the mixed set-valued vector IQVI and the vector inverse mixed quasivariational inequality problems, three gap functions were provided, respectively. Using generalized f -projection operator and three gap functions, scholars obtained error bounds of the generalized vector IQVI and the vector inverse mixed quasivariational inequality problems under the Lipschitz continuity and strong monotonicity of the underlying mappings [7][8][9] It can be seen that the research on the model of the IQVI problem is relatively active and has a wide application. However, the uniqueness of the IQVI problem is still few.…”