On the refinements of the Jensen-Steffensen inequality

On the refinements of the Jensen-Steffensen inequality

<p>Abstract</p> <p>In this paper, we extend some old and give some new refinements of the Jensen-Steffensen inequality. Further, we investigate the log-convexity and the exponential convexity of functionals defined via these inequalities and prove monotonicity property of the gener...

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Bibliographic Details
Main Authors: Khalid Sadia, Pe&#269;ari&#263; Josip, Franji&#263; Iva
Format: Article
Language:English
Published: SpringerOpen 2011-01-01
Series:Journal of Inequalities and Applications
Subjects:
Jensen-Steffensen inequality
refinements
exponential and logarithmic convexity
mean value theorems
Online Access:http://www.journalofinequalitiesandapplications.com/content/2011/1/12
Description
Summary:<p>Abstract</p> <p>In this paper, we extend some old and give some new refinements of the Jensen-Steffensen inequality. Further, we investigate the log-convexity and the exponential convexity of functionals defined via these inequalities and prove monotonicity property of the generalized Cauchy means obtained via these functionals. Finally, we give several examples of the families of functions for which the results can be applied.</p> <p>2010 <it>Mathematics Subject Classification</it>. 26D15.</p>
ISSN:1025-5834
1029-242X

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