An Equivalence between the Limit Smoothness and the Rate of Convergence for a General Contraction Operator Family

Maxim J. Goldberg and Seonja Kim

Abstract and Applied Analysis, 2020, vol. 2020, 1-5

Abstract:

Let be a topological space equipped with a complete positive - finite measure and a subset of the reals with as an accumulation point. Let be a nonnegative measurable function on which integrates to in each variable. For a function and , define . We assume that converges to in , as in . For example, is a diffusion semigroup (with ). For a finite measure space and , select real-valued , defined everywhere, with . Define the distance by . Our main result is an equivalence between the smoothness of an function (as measured by an - Lipschitz condition involving and the distance ) and the rate of convergence of to .

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:8866826

DOI: 10.1155/2020/8866826

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