Continued fractions built from convex sets and convex functions

Molchanov, Ilya (2015). Continued fractions built from convex sets and convex functions. Communications in contemporary mathematics, 17(5), p. 1550003. World Scientific Publishing 10.1142/S0219199715500030

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In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Molchanov, Ilya

Subjects:

500 Science > 510 Mathematics

ISSN:

1793-6683

Publisher:

World Scientific Publishing

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

28 Oct 2015 14:28

Last Modified:

14 Oct 2019 13:02

Publisher DOI:

10.1142/S0219199715500030

ArXiv ID:

1405.2779

BORIS DOI:

10.7892/boris.72282

URI:

https://boris.unibe.ch/id/eprint/72282

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