| In recent years, variational inequalities have been generalized and extended in many different fields, such as optimal control, electrical networks, transportation, finance, economics, structural analysis, optimization and operations research. Well-posedness is a classical notion in optimization problems and variational ineq- ualities theory, and it has had the profound influence on optimization problems and vari- ational inequalities theory. The well-posedness of variational inequality is to study the represent of the solution. Specially speaking, it considers if there has a subsequence of the approximating sequence converging to one of the solutions for the problem.Therefore, well-posedness of variational inequality plays an important part in the convergence of numerical methods.This paper studiesα-well-posedness for mixed quasi-variational-like inequality problems from the following aspects:1. Summarize the significance of academic research and researching current situation ofα-Well-Posedness for variational inequality.2. Introduce the related knowledge of set-valued map and mixed quasi-variational-like inequality basic which are involved in this paper.3. Ceng et al. introduced the the concepts of well-posedness and L-well-posedness for mixed quasi-variational-like inequality. Inspired by Ceng et al., we define the concepts ofα-well-posedness,α-well-posedness in the generalized sense, L-α-well-posedness, and L-α-well-posedness in the generalized sense for mixed quasi-variational-like inequality problems, extend Ceng's conclusions toα-well-posedness, L-α-well- posedness,α-well-posedness in the generalized sense, and L-α-well-posedness in the generalized sense for mixed quasi-variational-like inequality problems, and investigate some metric characterizations of these four kinds of well-posedness for mixed quasi-variational-like inequality problems. |
