Set Valued Mappings on the Reals

Weighted Variational Inequalities with Set-valued Mappings

Because of their applications in economics, game theory, mathematical physics, operations research and other areas, many classes of vector variational inequalities were intensively studied. For existence of solutions, resolution methods or equivalence with equilibrium and optimization problems see, for example, [11], [14], [15], [19], [17] and the references therein. For the study of variationa...

A Sard Theorem for Set-Valued Mappings∗†

If F is a set-valued mapping from IRn into IRm with closed graph, then y ∈ IRm is a critical value of F if for some x with y ∈ F (x), F is not metrically regular at (x, y). We prove that the set of critical values of a set-valued mapping whose graph is a definable (tame) set in an o-minimal structure containing additions and multiplications is a set of dimension not greater than m − 1 (resp. a ...

Fixed Point Theorems for Set-valued Mappings

Stationary Points for Set-valued Mappings on Two Metric Spaces

We give stationary point theorems of set-valued mappings in complete and compact metric spaces. The results in this note generalize a few results due to Fisher. 2000 Mathematics Subject Classification. 54H25.

On stationary points of nonexpansive set-valued mappings

*Correspondence: [email protected] 1Dpto. de Análisis Matemático, IMUS (Instituto Matemático de la Universidad de Sevilla), Universidad de Sevilla, C/Tarfia s/n, 41012 Sevilla, Spain Full list of author information is available at the end of the article Abstract In this paper we deal with stationary points (also known as endpoints) of nonexpansive set-valued mappings and show that the existence of...