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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Main Authors:	Khalid Sadia, Pečarić Josip, Franjić 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

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spelling	doaj-ad5f024d57dd4939baf9ba2927ee90b72020-11-24T20:47:26ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2011-01-012011112On the refinements of the Jensen-Steffensen inequalityKhalid SadiaPečarić JosipFranjić Iva<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> http://www.journalofinequalitiesandapplications.com/content/2011/1/12Jensen-Steffensen inequalityrefinementsexponential and logarithmic convexitymean value theorems
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Khalid Sadia Pečarić Josip Franjić Iva
spellingShingle	Khalid Sadia Pečarić Josip Franjić Iva On the refinements of the Jensen-Steffensen inequality Journal of Inequalities and Applications Jensen-Steffensen inequality refinements exponential and logarithmic convexity mean value theorems
author_facet	Khalid Sadia Pečarić Josip Franjić Iva
author_sort	Khalid Sadia
title	On the refinements of the Jensen-Steffensen inequality
title_short	On the refinements of the Jensen-Steffensen inequality
title_full	On the refinements of the Jensen-Steffensen inequality
title_fullStr	On the refinements of the Jensen-Steffensen inequality
title_full_unstemmed	On the refinements of the Jensen-Steffensen inequality
title_sort	on the refinements of the jensen-steffensen inequality
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1025-5834 1029-242X
publishDate	2011-01-01
description	<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>
topic	Jensen-Steffensen inequality refinements exponential and logarithmic convexity mean value theorems
url	http://www.journalofinequalitiesandapplications.com/content/2011/1/12
work_keys_str_mv	AT khalidsadia ontherefinementsofthejensensteffenseninequality AT pe269ari263josip ontherefinementsofthejensensteffenseninequality AT franji263iva ontherefinementsofthejensensteffenseninequality
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On the refinements of the Jensen-Steffensen inequality

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