A fixed point theorem with application to abstract economy (Q2789182)

In this paper, the authors prove, via a suitable KKM theorem, a new fixed point theorem on an l.c.-space \((X,\mathcal U,\mathcal B)\), thereby providing a general version of a result due to \textit{C. D. Horvath} [J. Math. Anal. Appl. 156, No. 2, 341--357 (1991; Zbl 0733.54011)]. Next, as an application, they establish their main existence theorem for noncompact abstract economies \(\Omega:=(X_\alpha, A_\alpha, B_\alpha, P_\alpha)_{\alpha\in I}\) involving \(\mathcal U_\theta\)-majorized set-valued mappings; the number of agents is possibly infinite, and \(X:=\prod_{\alpha\in I}X_{\alpha}\).