On the Equivalence between Perov Fixed Point Theorem and Banach Contraction Principle

There are many results in the fixed point theory that were presented as generalizations of Banach theorem and other well-known fixed point theorems, but later proved equivalent to these results. In this article we prove that Perov’s existence result follows from Banach theorem by using renormization...

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Bibliographic Details
Published in:Filomat 2017-01, Vol.31 (11), p.3137-3146
Main Author: Cvetkovic, Marija
Format: Article
Language:English
Subjects:
Banach space
Diagonal lemma
Equivalence relation
Mathematical constants
Mathematical theorems
Matrices
Perceptron convergence procedure
Space based observatories
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Summary:There are many results in the fixed point theory that were presented as generalizations of Banach theorem and other well-known fixed point theorems, but later proved equivalent to these results. In this article we prove that Perov’s existence result follows from Banach theorem by using renormization of normal cone and obtained metric. The observed estimations of approximate point given by Perov, could not be obtained from consequences of Banach theorem on metric spaces.
ISSN:0354-5180
2406-0933
DOI:10.2298/FIL1711137C