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Continued fractions built from convex sets and convex functions

Ilya Molchanov

Institute of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland

https://doi.org/10.1142/S0219199715500030Cited by:13 (Source: Crossref)

Abstract

In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalization 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.

Keywords:

AMSC: 46B10, 06F05, 11J70, 20M14, 26B25, 44A15, 52A22, 52A41

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