Abstract
In Section 1.2 three conditions were imposed on ϕ which were the basis of all the proofs up to now. In this chapter we will relax Conditions I and II and will show that in a way III cannot be relaxed without changing the definition of ω r ϕ (f,t) p . For ϕ(x) ~ xβ(0) where β(0) < 0 and ϕ(x) ~ xβ(∞) where β(∞) > 1 we will provide such a change.
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© 1987 Springer-Verlag New York Inc.
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Ditzian, Z., Totik, V. (1987). More General Step-Weight Functions ϕ. In: Moduli of Smoothness. Springer Series in Computational Mathematics, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4778-4_6
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DOI: https://doi.org/10.1007/978-1-4612-4778-4_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9151-0
Online ISBN: 978-1-4612-4778-4
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