Abstract
The Banach contraction principle was generalized by Perov (see Perov-Kibenko [40]) for contractive maps on spaces endowed with vector-valued metrics. Also, Granas [25] proved that the property of having a fixed point is invariant under homotopy for contractions on complete metric spaces. This result was completed in Precup [50] (see also O’Regan-Precup [38] and Precup [51], [52]) by an iterative procedure of discrete continuation along the fixed points curve. This chapter presents a variant for contractive maps on spaces with vector-valued metrics, first given in Precup [54].
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© 2002 Springer Science+Business Media Dordrecht
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Precup, R. (2002). The Discrete Continuation Principle. In: Methods in Nonlinear Integral Equations. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9986-3_11
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DOI: https://doi.org/10.1007/978-94-015-9986-3_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6114-0
Online ISBN: 978-94-015-9986-3
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