Abstract
AbstractThis is a continuation of Chapter 10 among others, still we study global smoothness preservation over R. Here are given sufficient conditions, so that the derivatives of general operators, examined in Chapter 10, enjoy the same nice properties as their originals. A sufficient condition is also given so that the “global smoothness preservation” related inequality becomes sharp. At the end of the chapter several applications are presented, where the derivatives of the very general specialized operators are shown to fulfill all the related properties. In particular it is established that they preserve continuous probability density functions. Here we follow the basic study done by the first author [21].KeywordsGeneral OperatorApproximation TheoryNice PropertyBernstein PolynomialRelated InequalityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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