In this note, we show that when the function f(x) is convex in the interval (0, ∞) for any natural number n,

is true. Using this, we give upper bounds for  and  

convex, convex function, analysis, upper bound, interval (0, ∞).

Received: January 3, 2023;  Revised: January 31, 2023;  Accepted: February 3, 2023

How to cite this article: Masakazu Nihei, On certain inequalities for convex functions, Far East Journal of Mathematical Education 24 (2023), 9-12. http://dx.doi.org/10.17654/0973563123004

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] G. H. Hardy, Pure Mathematics, Cambridge University Press, 1967.
[2] Sze-Tsen Hu, Calculus, Markham Publishing Company, Chicago, 1970.