Necessary and sufficient conditions for large contractions in fixed point theory

Burton, Theodore A. and Purnaras, Ioannis K.: Necessary and sufficient conditions for large contractions in fixed point theory. Electronic journal of qualitative theory of differential equations 94. pp. 1-24. (2019)

[img] Cikk, tanulmány, mű
ejqtde_2019_094.pdf

Download (503kB)

Abstract

Many problems in integral and differential equations involve an equation in which there is almost a contraction mapping. Through some type of transformation we arrive at an operator of the form H(x) = x − f(x). The paper contains two main parts. First we offer several transformations which yield that operator. We then offer necessary and sufficient conditions to ensure that the operator is a large contraction. These operators yield unique fixed points. A partial answer to a question raised in [D. R. Smart, Fixed point theorems, Cambridge University Press, Cambridge, 1980] is given. The last section contains examples and applications.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 94
Page Range: pp. 1-24
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.94
Uncontrolled Keywords: Differenciaegyenlet, Integrálegyenlet
Additional Information: Bibliogr.: p. 23-24. ; összefoglalás angol nyelven
Date Deposited: 2020. Jan. 27. 14:02
Last Modified: 2020. Jan. 27. 14:02
URI: http://acta.bibl.u-szeged.hu/id/eprint/66361

Actions (login required)

View Item View Item