A generalized modulus of smoothness

Authors:
Borislav R. Draganov and Kamen G. Ivanov

Journal:
Proc. Amer. Math. Soc. **142** (2014), 1577-1590

MSC (2010):
Primary 41A25; Secondary 41A15, 41A27

Published electronically:
February 6, 2014

MathSciNet review:
3168465

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Abstract | References | Similar Articles | Additional Information

Abstract: We construct moduli of smoothness that generalize the well-known classical moduli and possess similar properties. They are related to a linear differential operator just as the classical moduli are related to the ordinary derivative. The generalized moduli are used to characterize the approximation error of the corresponding -splines in , .

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Additional Information

**Borislav R. Draganov**

Affiliation:
Department of Mathematics and Informatics, University of Sofia, 5 James Bourchier Boulevard, 1164 Sofia, Bulgaria – and – Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, bl. 8 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria

Email:
bdraganov@fmi.uni-sofia.bg

**Kamen G. Ivanov**

Affiliation:
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, bl. 8 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria

Email:
kamen@math.bas.bg

DOI:
http://dx.doi.org/10.1090/S0002-9939-2014-11884-3

Keywords:
Modulus of smoothness,
$K$-functional,
rate of convergence,
$L$-spline,
linear operator

Received by editor(s):
February 11, 2012

Received by editor(s) in revised form:
May 7, 2012, and May 30, 2012

Published electronically:
February 6, 2014

Additional Notes:
Both authors were supported by grant DDVU 02/30 of the Fund for Scientific Research of the Bulgarian Ministry of Education and Science.

Communicated by:
Walter Van Assche

Article copyright:
© Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.