Generalized 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 14 in Approximation Theory, 2000, pp 373-389 from Springer

Abstract: Abstract This chapter is a continuation and generalization of Chapter 10. Among others we further study global smoothness preservation over R. In particular, certain others, similar to those in Chapter 10, but more general integral operators are presented and studied. These operators arise in a natural way. And for all these are given sufficient conditions for: shift invariance, preservation of higher order global smoothness and sharpness of the related inequalities, convergence to the unit using the first modulus of continuity, shape preserving and preservation of continuous probabilistic distribution functions. Several examples of diverse, very general specialized operators are given fulfilling all the above listed properties. Here we follow the basic study done by both authors in [24].

Keywords: Related Inequality; Positive Linear Operator; Continuous Distribution Function; Listed Property; Shape Preserve (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_14

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DOI: 10.1007/978-1-4612-1360-4_14

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