On quasi-continuous iteration groups on the unit circle.

Piekarska, A.

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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...

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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 $ℱ = {F^{v} 𝕊^{1} ⟶ 𝕊^{1} v \in V}$ of homeomorphisms such that $F^{v_{1}} \circ F^{v_{2}} = F^{v_{1} + v_{2}}, v_{1}, v_{2} \in V,$ 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).

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