Displaying similar documents to “On quasi-continuous iteration groups on the unit circle.”

Some convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operators

Müzeyyen Ertürk, Faik Gürsoy (2019)

Mathematica Bohemica

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We study some qualitative features like convergence, stability and data dependency for Picard-S iteration method of a quasi-strictly contractive operator under weaker conditions imposed on parametric sequences in the mentioned method. We compare the rate of convergence among the Mann, Ishikawa, Noor, normal-S, and Picard-S iteration methods for the quasi-strictly contractive operators. Results reveal that the Picard-S iteration method converges fastest to the fixed point of quasi-strictly...

The structure of disjoint iteration groups on the circle

Krzysztof Ciepliński (2004)

Czechoslovak Mathematical Journal

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The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle 𝕊 1 , that is, families ℱ = { F v 𝕊 1 ⟶ 𝕊 1 v ∈ V } of homeomorphisms such that F v 1 ∘ F v 2 = F v 1 + v 2 , v 1 , v 2 ∈ V , and each F v either is the identity mapping or has no fixed point ( ( V , + ) is an arbitrary 2 -divisible nontrivial (i.e., c a r d V > 1 ) abelian group).