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Advances in Inequalities and Applications ISSN 2050-7461

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Adv. Inequal. Appl. 2014 (2014), Article ID 29

A proof of Jensen’s inequality through a new Steffensen’s inequality

Mohammed M. Iddrisu, Christopher A. Okpoti, Kazeem A. Gbolagade

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Abstract

In this paper, we present more proofs of the new Steffensen’s inequality for convex functions. First, we provide separate proofs for continuous functions followed by a general proof for all L1([0,1]) functions. The last part is dedicated to the proof of the well known Jensen’s inequality using the new inequality.

Published
22 July 2014
Volume
2014 (2014)
License
CC BY 3.0

Copyright © 2014 Mohammed M. Iddrisu, Christopher A. Okpoti, Kazeem A. Gbolagade. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

M. M. Iddrisu, C. A. Okpoti, K. A. Gbolagade, A proof of Jensen’s inequality through a new Steffensen’s inequality, Adv. Inequal. Appl. 2014 (2014), 29.

BibTeX
@article{Iddrisu2014,
  author  = {Iddrisu, Mohammed M. and Okpoti, Christopher A. and Gbolagade, Kazeem A.},
  title   = {A proof of Jensen’s inequality through a new Steffensen’s inequality},
  journal = {Adv. Inequal. Appl.},
  volume  = {2014},
  year    = {2014},
  pages   = {29},
  doi     = {}
}