The Discrete Continuation Principle

Radu Precup
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Radu Precup: Babeş-Bolyai University, Department of Applied Mathematics

Chapter Chapter 10 in Methods in Nonlinear Integral Equations, 2002, pp 151-162 from Springer

Abstract: 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].

Date: 2002
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DOI: 10.1007/978-94-015-9986-3_11

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