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On moduli of smoothness of k-monotone functions and applications

Published online by Cambridge University Press:  01 January 2009

KIRILL KOPOTUN
KIRILL KOPOTUN*
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada. e-mail: kopotunk@cc.umanitoba.ca
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Abstract

Let k be the set of all k-monotone functions on (−1, 1), i.e., those functions f for which the kth divided differences [x0,. . ., xk; f] are nonnegative for all choices of (k+1) distinct points x0,. . .,xk in (−1, 1). We obtain estimates (which are exact in a certain sense) of kth Ditzian–Totik q-moduli of smoothness of functions in k∩p(−1, 1), where 1 ≤ q < p ≤ ∞, and discuss several applications of these estimates.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 1 , January 2009 , pp. 213 - 223
Copyright
Copyright © Cambridge Philosophical Society 2008

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