JNCA: Fixed point theory of approximable multimaps



	Volume 9, Number 2, August 2008, pp. 169-179
Sehie Park
Key words:
Multimap (map), $(U,V)$-approximative continuous selection, approachable map, approximable map, Leray-Schauder alternative
Mathematices Subject Classification: Primary 47H10, 54C60; Secondary 54H25, 49J35, 49K35, 52A07, 55M20


	Abstract:
	We show that, for a subset X of a t.v.s. E, any compact closed approachable multimap T : X \multimap X has a fixed point if the map has Klee approximable range. As applications of this theorem, we notice that the local convexity of E in many known results can be replaced by more general conditions, and obtain a number of generalizations of known fixed point or relevant theorems, all related to compact closed approachable or approximable multimaps.