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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

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 $ L$ just as the classical moduli are related to the ordinary derivative. The generalized moduli are used to characterize the approximation error of the corresponding $ L$-splines in $ L_p [a,b]$, $ 1\le p\le \infty $.


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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.



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