Continued fractions built from convex sets and convex functions
نویسنده
چکیده
In a partially ordered semigroup with the duality (or polarity) transform, it is possible 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 ArtsteinAvidan–Milman transforms. AMS Classification: 46B10, 06F05, 11J70, 20M14, 26B25, 44A15, 52A22, 52A41
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