Section theorems, coincidence theorems and intersection theorems on \(H\)- spaces with applications (Q1310359)

This paper is devoted to the study of section theorems, coincidence theorems and intersection theorems in \(H\)-space, i.e. in an ordered space \((X,\{ \Gamma_ A\})\) such that \(X\) is a topological space, and \(\Gamma_ A\) is a family of nonempty contractible sets indexed by all the finite subsets \(A\) of \(X\) with the following property: \(A\subset A'\Rightarrow\Gamma_ A\subset\Gamma_{A'}\) (e.g. \(\Gamma_ A=\text{conv} A)\). After definitions of \(H\)-convexity, \(H\)-compactness, \(H\)-KKM-mapping and \(H\)-affine mapping, the main theorems are proved. They are: 3 section theorems, 1 intersection theorem and 2 coincidence theorems. Some applications of the above theorems to the study of the existence of solutions of some variational inequalities and minimax inequalities are presented. All theorems generalize and extend some earlier known formulations of the corresponding theorems (e.g. results by Ky Fan, Dugundji-Granas, Yen, Lassonde, Horvath, Bardaro-Ceppitelli, and others).