Global Smoothness Preservation by Multivariate 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 8 in Approximation Theory, 2000, pp 251-263 from Springer

Abstract: Abstract In this chapter we discuss the global smoothness preservation by some multivariate approximating operators. By extending a fundamental result of Khan and Peters, we establish a general result for operators having the splitting property. Furthermore, we show more complete inequalities for Bernstein operators on the k-dimensional simplex and cube, formulate a certain transfer principle for tensor product operators, and apply an earlier related result in the context of stochastic approximation. Here we follow the basic study done by the first author, Cottin and Gonska [23].

Keywords: Tensor Product; Banach Lattice; Stochastic Approximation; Compact Convex Subset; Transfer Principle (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_8

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DOI: 10.1007/978-1-4612-1360-4_8

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