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Characterization Theorems for the Approximation by a Family of Operators

✍ Scribed by Detlef H. Mache; Ding X. Zhou

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
671 KB
Volume
84
Category
Article
ISSN
0021-9045

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✦ Synopsis

The intention of this paper is to study a family of positive linear approximation operators relating to most of the well known Bernstein-type operators. These operators depend on a parameter. We give some characterization theorems to show that the operators corresponding to different parameters can be quite different. The direct and converse results make use of the Ditzian Totik modulus of smoothness. 1996 Academic Press, Inc. and p n, k (x)=( n k ) x k (1&x) n&k , x # I, n # N. article no. 0012 145 0021-9045Γ‚96 12.00

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## Abstract We consider a class of abstract evolution problems characterized by the sum of two unbounded linear operators __A__ and __B__, where __A__ is assumed to generate a positive semigroup of contractions on an L^1^‐space and B is positive. We study the relations between the semigroup generat