Continuation Theory for Contractions on Spaces with Two Vector-Valued Metrics

Authors: O'Regan D.1; Precup R.2

Source: Applicable Analysis, Volume 82, Number 2, 2003 , pp. 131-144(14)

Publisher: Taylor and Francis Ltd

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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.

Keywords: Contraction; Fixed point; Operator equation; Hammerstein integral equations

Document Type: Research article

DOI: 10.1080/000368103763297438

Affiliations: 1: Department of Mathematics, National University of Ireland, Galway, Ireland 2: Department of Applied Mathematics, Babescedil-Bolyai University, Cluj, Romania-Bolyai University, Cluj, Romania">

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