Applications of the generalized Knaster-Kurakowski-Mazurkiewicz theorem to variational inequalities
The paper generalizes a result of \textit{M. Lassonde} [ibid. 97, 151-201 (1983; Zbl 0527.47037)] on variational inequalities by using the extensions of the Knaster-Kuratowski-Mazurkiewicz (KKM) theorem [\textit{B. Knaster}, \textit{C. Kuratowski} and \textit{S. Mazurkiewicz}, Fundam. Math. 14, 132-137 (1929)]. Inequalities are considered in the form \(\cap_{x\in X}F(x)\neq \emptyset\), where \(F: X\to X\) is an H-KKM multifunction operating in H-space \((X,\{\Gamma_ A\})\). Further inequalities for functions with values in a Riesz space are solved.
Knaster-Kuratowski-Mazurkiewicz (KKM) theorem
scientific article; zbMATH DE number 4115372
scientific article