Existence theorems of solutions for a kind of quasi-variational inequalities with monotone type multivalued mapping
Let \(X\) be a topological space and \(\{F_A\}\) be a family of nonempty contractible subsets of \(X\) indexed by a nonempty finite subset \(A\) of \(X\). The pair \((X,\{F_A\})\) is called an \(H\)-space. Let \(Y\) be a topological space, \(\varphi: X\times Y\times X\to R\) and \(T: X\to 2^Y\) be a \(\varphi\)-monotone multivalued mapping with nonempty values. The main results of this paper are two existence theorems for the following quasivariational inequality: find \(u_0\in X\) such that \(\sup\{\varphi(v,w,u_0): w\in T(u_0)\}\geq 0\), for all \(v\in X\).
\(\varphi\)-monotone multivalued mapping
scientific article; zbMATH DE number 1391571
scientific article