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On moduli of smoothness of k-monotone functions and applications
Published online by Cambridge University Press: 01 January 2009
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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