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Well-posedness by perturbations of variational-hemivariational inequalities with perturbations

Ceng Lu-Chuan (Department of Mathematics, Shanghai Normal University, China + Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China)
Gupta Himanshu (Department of Mathematics, Aligarh Muslim University, Aligarh, India)
Wen Ching-Feng (General Education Center Kaohsiung Medical University Kaohsiung, Taiwan)

In this paper, we consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a class of variational-hemivariational inequalities with perturbations in Banach spaces, which includes as a special case the class of mixed variational inequalities. Under very mild conditions, we establish some metric characterizations for the well-posed variational-hemivariational inequality, and show that the well-posedness by perturbations of a variational-hemivariational inequality is closely related to the well-posedness by perturbations of the corresponding inclusion problem. Furthermore, in the setting of finite-dimensional spaces we also derive some conditions under which the variational-hemivariational inequality is strongly generalized well-posed-like by perturbations.

Keywords: variational-hemivariational inequality, inclusion problem, well-posedness by perturbations, uniqueness, approximating sequence