Topological Methods in Nonlinear Analysis

An extension of Krasnoselskiĭ's fixed point theorem for contractions and compact mappings

George L. Karakostas

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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.

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Topol. Methods Nonlinear Anal., Volume 22, Number 1 (2003), 181-191.

First available in Project Euclid: 30 September 2016

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Karakostas, George L. An extension of Krasnoselskiĭ's fixed point theorem for contractions and compact mappings. Topol. Methods Nonlinear Anal. 22 (2003), no. 1, 181--191.

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