Journal of the
Korean Mathematical Society JKMS

In this paper, using proximal-point mappings technique of $R$-accretive mappings and the property of the fixed point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of the system of parametric generalized quasi-variational inclusions involving $R$-accretive mappings in real uniformly smooth Banach space. Further under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to parameters. The technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in [3, 23, 24, 32, 33, 34].

Keywords: system of parametric generalized quasi-variational inclusions, proximal-point mappings, $R$-accretive mappings, strongly accretive mappings, mixed Lipschitz continuous, $H$-Lipschitz continuous

MSC numbers: 49J40, 65K10