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.
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