Krasnoselskii's theorem in generalized Banach spaces and application

The purpose of this paper is to extend Krasnoselskii's fixed point theorem to the case of generalized Banach spaces for singlevalued and multivalued operators. As applications, we will give some existence results for abstract system of Fredholm-Volterra type differential equations and inclusion...

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Bibliographic Details
Published inElectronic journal of qualitative theory of differential equations Vol. 2012; no. 85; pp. 1 - 20
Main Authors Petre, Ioan Radu, Petrusel, Adrian
Format Journal Article
LanguageEnglish
Published University of Szeged 01.10.2012
Subjects
a-contraction
compact operator
complete generalized metric space
contraction principle
fixed point
fredholm-volterra equation
fredholm-volterra inclusion
generalized banach space
generalized contraction
generalized metric space
integral equation
integral inclusion
iterative method
krasnoselskii theorem
matrix convergent to zero
multivalued operator
perov theorem
picard operator
relatively compact operator
schauder theorem
singlevalued operator
sum of two operators
vector-valued metric
vector-valued norm
weakly picard operator
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Summary:The purpose of this paper is to extend Krasnoselskii's fixed point theorem to the case of generalized Banach spaces for singlevalued and multivalued operators. As applications, we will give some existence results for abstract system of Fredholm-Volterra type differential equations and inclusions.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2012.1.85