Leray–Schauder and Krasnoselskii results for multivalued maps defined on pseudo-open subsets of a Fréchet space

doi:10.1016/j.aml.2005.11.017

Applied Mathematics Letters

Volume 19, Issue 12, December 2006, Pages 1327-1334

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Abstract

New Leray–Schauder alternatives and Krasnoselskii expansion and compression theorems are presented for multivalued maps defined on subsets of a Fréchet space $E$ . The proof relies on the notion of a pseudo-open set and on viewing $E$ as the projective limit of a sequence of Banach spaces.

Keywords

Leray–Schauder alternative

Krasnoselskii expansion

Multivalued maps

Pseudo-open set

Projective limit