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Perov-type contractions. (English) Zbl 1496.54034

Daras, Nicholas J. (ed.) et al., Approximation and computation in science and engineering. Cham: Springer. Springer Optim. Appl. 180, 167-215 (2022).
Summary: Fixed point theory is rapidly growing in various directions, so the goal of this chapter is to collect and underline recent results on Perov-type contractions and talk about various generalizations of this result. Perov contraction is defined on generalized metric space firstly introduced by Russian mathematician A. I. Perov [Priblizhen. Metody Reshen. Differ. Uravn. 2, 115–134 (1964; Zbl 0196.34703)]. The main difference and strength of this result is in changed view on contractive constant since, in Perov results, that role is played by a matrix with positive entries. The question is what do we gain in this case? And also can we talk about scientific novelty of this concrete results and all other generalizations published in the last 10 years? We will try to answer at least partially on these questions and gather most important results regarding Perov contractions.
For the entire collection see [Zbl 1485.65002].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces

Citations:

Zbl 0196.34703
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Full Text: DOI

References:

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