Computational Methods and Function Theory 1 (2001), No. 2, 417--432
Copyright Heldermann Verlag 2001
Sorin G. Gal
galso@uoradea.ro, Department of Mathematics, University of Oradea, Str. Armatei Române 5, 3700 Oradea, Romania.
In this paper we study classes of convolution-type complex operators for analytic functions on the open unit disk $\mathbb{D}$ which are continuous on~$\bar{\mathbb{D}}$. Their simple forms present three advantages: firstly, estimates with rates in terms of higher moduli of smoothness (or of best approximation) and explicit constants can easily be obtained, secondly we can prove global smoothness preservation properties with (best) constants for them, and thirdly, some shape preserving properties hold.
Keywords: Convolution-type operators, complex approximation, global smoothness preservation, moduli of smoothness, shape preserving approximation.
MSC 2000: 30E10, 30C45, 41A10, 41A25, 41A99.
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