On the Well-Posedness of Generalized Hemivariational Inequalities and Inclusion Problems in Banach Spaces
نویسندگان
چکیده
In the present paper, we generalize the concept of well-posedness to a generalized hemivariational inequality, give some metric characterizations of the α-well-posed generalized hemivariational inequality, and derive some conditions under which the generalized hemivariational inequality is strongly α-well-posed in the generalized sense. Also, we show that the α-well-posedness of the generalized hemivariational inequality is equivalent to the α-well-posedness of the corresponding inclusion problem.
منابع مشابه
Some Equivalence Results for Well-Posedness of Generalized Hemivariational Inequalities with Clarke’s Generalized Directional Derivative
In this paper, we are devoted to exploring conditions of well-posedness for generalized hemivariational inequalities with Clarke’s generalized directional derivative in reflexive Banach spaces. By using some equivalent formulations of the generalized hemivariational inequality with Clarke’s generalized directional derivative under different monotonicity assumptions, we establish two kinds of co...
متن کاملHadamard Well-posedness for a Family of Mixed Variational Inequalities and Inclusion Problems
In this paper, the concepts of well-posednesses and Hadamard well-posedness for a family of mixed variational inequalities are studied. Also, some metric characterizations of them are presented and some relations between well-posedness and Hadamard well-posedness of a family of mixed variational inequalities is studied. Finally, a relation between well-posedness for the family of mixed variatio...
متن کاملExistence and Uniqueness Results for a Nonstandard Variational-Hemivariational Inequalities with Application
This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...
متن کاملWell-Posedness for a Class of Strongly Mixed Variational-Hemivariational Inequalities with Perturbations
In this paper, the concept of well-posedness for a minimization problem is extended to develop the concept of well-posedness for a class of strongly mixed variationalhemivariational inequalities with perturbations which includes as a special case the class of variational-hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed strongly mixed...
متن کاملWell-Posedness by Perturbations for Variational-Hemivariational Inequalities
We generalize the concept of well-posedness by perturbations for optimization problem to a class of variational-hemivariational inequalities. We establish some metric characterizations of the well-posedness by perturbations for the variational-hemivariational inequality and prove their equivalence between the well-posedness by perturbations for the variational-hemivariational inequality and the...
متن کامل