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- Title
Continued fractions built from convex sets and convex functions.
- Authors
Molchanov, Ilya
- 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.
- Subjects
CONTINUED fractions; CONVEX sets; CONVEX functions; STOCHASTIC convergence; ADDITION (Mathematics)
- Publication
Communications in Contemporary Mathematics, 2015, Vol 17, Issue 5, p-1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199715500030