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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 30 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1475266325

Mathematical Reviews number (MathSciNet)
MR2037274

Zentralblatt MATH identifier
1067.47073

Citation

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. https://projecteuclid.org/euclid.tmna/1475266325


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