Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606922 | Journal of Approximation Theory | 2015 | 16 Pages |
Abstract
We consider two-sided continued fractions in Banach algebras, that is K=b0+a1(b1+a2(b2+…)−1c2)−1c1,K=b0+a1(b1+a2(b2+…)−1c2)−1c1, where the coefficients bn,an,cnbn,an,cn are elements of some Banach algebra. We prove convergence criteria which are exact generalizations of the well-known Pringsheim-type convergence criteria for complex continued fractions, and state a result concerning the rate of convergence. Both convergence criteria and error bounds improve all known results.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hendrik Baumann,