An extension of Krasnoselskii's fixed point theorem for contractions and compact mappings
Keywords
Banach space, equicontractions, fixed point theoremAbstract
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.Downloads
Published
2003-09-01
How to Cite
1.
KARAKOSTAS, George L. An extension of Krasnoselskii’s fixed point theorem for contractions and compact mappings. Topological Methods in Nonlinear Analysis. Online. 1 September 2003. Vol. 22, no. 1, pp. 181 - 191. [Accessed 28 March 2024].
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