CUBO A Mathematical Journal Vol.12, N°03, (139–151). October 2010

Some Generalizations of Mulit-Valued Version of Schauder’s Fixed Point Theorem with Applications

BAPURAO C. DHAGE

Kasubai, Gurukul Colony, Ahmedpur – 413515, Distr. Latur, Maharashtra, India email: bcdhage@yahoo.co.in

ABSTRACT

In this article, a generalization of a Kakutani-Fan fixed point theorem for multi-valued mappings in Banach spaces is proved under weaker upper semi-continuity condition and it is further applied to derive a generalized version of Krasnoselskii’s fixed point theorem and some nonlinear alternatives of Leray-Schauder type for multi-valued closed mappings in Banach spaces.

Key words and phrases: Multi-valued mappings, fixed point theorem, nonlinear alternative.

RESUMEN

En este artículo probamos una generalización para el teorema del punto fijo de Kakutani- Fan para aplicaciones multi-valuadas en espacios de Banach, bajo condición de semi-continuidad superior debil. Este resultado es aplicado para obtener una versión generalizada del teorema del punto fijo Krasnoselskii y algunas alternativas de tipo Leray-Schauder para aplicaciones multi-valuadas cerradas en espacios de Banach.

Math. Subj. Class.: 47H10.

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