On the growth of real functions and their derivatives

Jürgen Grahl; Shahar Nevo

doi:10.14321/realanalexch.43.2.0333

On the growth of real functions and their derivatives

Jürgen Grahl, Shahar Nevo

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We show that for any k-times differentiable function f: [a,∞) → R, any integer q ≥ 0 and any α > 1 the inequality holds and that this result is best possible in the sense that log _q x cannot be replaced by (log _q x) ^β with any β > 1.

Original language	English
Pages (from-to)	333-346
Number of pages	14
Journal	Real Analysis Exchange
Volume	43
Issue number	2
DOIs	https://doi.org/10.14321/realanalexch.43.2.0333
State	Published - 2018

Keywords

Differential inequalities
Growth of real-valued functions

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.14321/realanalexch.43.2.0333

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title = "On the growth of real functions and their derivatives",

abstract = " We show that for any k-times differentiable function f: [a,∞) → R, any integer q ≥ 0 and any α > 1 the inequality holds and that this result is best possible in the sense that log q x cannot be replaced by (log q x) β with any β > 1.",

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AB - We show that for any k-times differentiable function f: [a,∞) → R, any integer q ≥ 0 and any α > 1 the inequality holds and that this result is best possible in the sense that log q x cannot be replaced by (log q x) β with any β > 1.

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DO - 10.14321/realanalexch.43.2.0333

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On the growth of real functions and their derivatives

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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