Differentiated Shift Invariant Univariate Integral Operators

George A. Anastassiou and Sorin G. Gal
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George A. Anastassiou: University of Memphis, Department of Mathematical Sciences
Sorin G. Gal: University of Oradea, Department of Mathematics

Chapter 12 in Approximation Theory, 2000, pp 325-345 from Springer

Abstract: Abstract This 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].

Keywords: General Operator; Approximation Theory; Nice Property; Bernstein Polynomial; Related Inequality (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1360-4_12

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DOI: 10.1007/978-1-4612-1360-4_12

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