Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-03T00:03:03.241Z Has data issue: false hasContentIssue false
  • English
  • Français

Two ways to generate monotonic sequences: convexity and ratios

Published online by Cambridge University Press:  17 February 2021

G. J. O. Jameson
G. J. O. Jameson*
Affiliation:
Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

Here we give an account of two appealingly simple techniques to generate monotonic sequences that were developed by the author and Grahame Bennett. Sadly, Bennett died in 2016 after a lifetime of distinguished contributions in the field of inequalities. This article is dedicated to him.

Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 562 , March 2021 , pp. 16 - 26
Check for updates
Copyright
© The Mathematical Association 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bennett, G. and Jameson, G. J. O., Monotonic averages of convex functions, J. Math. Anal. Appl. 252 (2000) pp. 410–43010.1006/jmaa.2000.7087CrossRefGoogle Scholar
Jichang, Kuang, Some extensions and refinements of Minc-Sathre inequality, Math. Gaz. 83 (March 1999) pp. 123–127.10.2307/3618705CrossRefGoogle Scholar
Bennett, G., Meaningful sequences, Houston J. Math. 33 (2007) pp. 555–580.Google Scholar
Minc, H. and Sathre, L., Some inequalities concerning (r!)1/r, Proc. Edinburgh Math. Soc. 14 (1964) pp. 41–46.10.1017/S0013091500011214CrossRefGoogle Scholar
Bromwich, T. J. I'A., An introduction to the theory of infinite series (1st edn.) MacMillan (1908).Google Scholar
Jameson, G. J. O., Monotonicity of the midpoint and trapezium estimates for integrals, Math. Gaz. 105 (March 2021) pp. 129–134.Google Scholar
Jameson, G. J. O., Monotonicity of weighted averages of convex functions, Math. Ineq. Appl., 23 (2020) pp. 425–432.Google Scholar