Weierstrass-Stone theorems for set-valued mappings

Fixed Point Theorems for Set-valued Mappings

Stone-Weierstrass type theorems for large deviations

We give a general version of Bryc’s theorem valid on any topological space and with any algebra A of real-valued continuous functions separating the points, or any wellseparating class. In absence of exponential tightness, and when the underlying space is locally compact regular and A constituted by functions vanishing at infinity, we give a sufficient condition on the functional Λ(·)|A to get ...

Stone-weierstrass Theorems for the Strict Topology

1. Let X be a locally compact Hausdorff space, E a (real) locally convex, complete, linear topological space, and (C*(X, E), ß) the locally convex linear space of all bounded continuous functions on X to E topologized with the strict topology ß. When E is the real numbers we denote C*(X, E) by C*(X) as usual. When E is not the real numbers, C*(X, E) is not in general an algebra, but it is a mod...

Some Fixed Point Theorems for Nonlinear Set-Valued Contractive Mappings

Minimax Theorems for Set-Valued Mappings under Cone-Convexities

and Applied Analysis 3 Lemma 2.4 see 9, Lemma 3.1 . Let X, Y, and Z be three topological spaces. Let Y be compact, F : X × Y ⇒ Z a set-valued mapping, and the set-valued mapping T : X ⇒ Z defined by T x ⋃ y∈Y F ( x, y ) , ∀x ∈ X. 2.2 a If F is upper semi-continuous on X × Y, then T is upper semi-continuous on X. b If F is lower semi-continuous onX, so is T. Lemma 2.5 see 9, Lemma 3.2 . Let Z be...