An extension of Krasnoselskii's fixed point theorem for contractions and compact mappings
Słowa kluczowe
Banach space, equicontractions, fixed point theoremAbstrakt
Let $X$ be a Banach space, $Y$ a metric space, $A\subseteq X$, $C\colon A\to Y$ a compact operator and $T$ an operator defined at least on the set $A\times C(A)$ with values in $X$. By assuming that the family $\{T(\cdot,y):y\in C(A)\}$ is equicontractive we present two fixed point theorems for the operator of the form $Ex:=T(x,C(x))$. Our results extend the well known Krasnosel'skiĭ's fixed point theorem for contractions and compact mappings. The results are used to prove the existence of (global) solutions of integral and integrodifferential equations.Pobrania
Opublikowane
2003-09-01
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1.
KARAKOSTAS, George L. An extension of Krasnoselskii’s fixed point theorem for contractions and compact mappings. Topological Methods in Nonlinear Analysis [online]. 1 wrzesień 2003, T. 22, nr 1, s. 181–191. [udostępniono 22.7.2024].
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