Real inequalities with applications to function theory
Published online by Cambridge University Press: 24 October 2008
Extract
Suppose that f(x) is non-negative for x ≥ 0 and let
In a recent paper (4) inequalities were proved relating fn(x) with the nth derivative f(n)(x) of f(x). However, the two main results, Theorems 3 and 4, were proved only for n = 1 and 2. In the first part of this paper we shall prove the corresponding results for all positive integral n under a slightly less restrictive hypothesis (Theorem 3). We shall then give an application showing that from the hypothesis f(x) ≤ μ(x) for all x it is sometimes possible to deduce f(n)(x) = O{μ(n)(x)} for a set of values x depending only on μ(x).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 2 , April 1954 , pp. 250 - 260
- Copyright
- Copyright © Cambridge Philosophical Society 1954
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