Continuation theory for contractions on spaces with two vector-valued metrics

Abstract

We develop a continuation theory for contractive maps on spaces with two vector-valued metrics. Applications are presented for systems of operator equations in Banach spaces and, in particular, for systems of abstract Hammerstein integral equations. The use of vector-valued metrics makes it possible for each equation of a system to have its own Lipschitz property, while the use of two such metrics makes it possible for the Lipschitz condition to be expressed with respect to an incomplete metric

Authors

Donal O’Regan
Department of Mathematics , National University of Ireland , Galway, Ireland

Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Contraction; Fixed Point Operator; EquationHammerstein; Integral Equations

Paper coordinates

D. O’Regan, R. Precup, Continuation theory for contractions on spaces with two vector-valued metrics, Appl. Anal. 82 (2003) no. 2, 131-144, https://doi.org/10.1080/0003681031000063784

PDF

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Journal

Applicable Analysis

0003-6811

Online ISSN

1563-504X

MR 1966853, Zbl 1034.54017