Some Simpson type integral inequalities for functions whose third derivatives are (α, m)- GA-convex functions

By using power-mean integral inequality and Hölder’s integral inequality, this paper establishes some new inequalities of Simpson type for functions whose three derivatives in absolute value are the class of (α, m)-geometric-arithmetically-convex functions. Finally, some applications to special mean...

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Main Authors:	YuJiao Li, TingSong Du
Format:	Article
Language:	English
Published:	SpringerOpen 2016-04-01
Series:	Journal of the Egyptian Mathematical Society
Subjects:	Convex function (α, m)-GA-convex functions Simpson type inequality
Online Access:	http://www.sciencedirect.com/science/article/pii/S1110256X15000516

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spelling	doaj-96d4a948f4d648899c1655d8dc98c06d2020-11-25T02:44:01ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2016-04-0124217518010.1016/j.joems.2015.05.009Some Simpson type integral inequalities for functions whose third derivatives are (α, m)- GA-convex functionsYuJiao Li0TingSong Du1Department of Mathematics, Science College, China Three Gorges University, Yichang 443002, ChinaDepartment of Mathematics, Science College, China Three Gorges University, Yichang 443002, ChinaBy using power-mean integral inequality and Hölder’s integral inequality, this paper establishes some new inequalities of Simpson type for functions whose three derivatives in absolute value are the class of (α, m)-geometric-arithmetically-convex functions. Finally, some applications to special means of positive real numbers have also been presented.http://www.sciencedirect.com/science/article/pii/S1110256X15000516Convex function(α, m)-GA-convex functionsSimpson type inequality
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	YuJiao Li TingSong Du
spellingShingle	YuJiao Li TingSong Du Some Simpson type integral inequalities for functions whose third derivatives are (α, m)- GA-convex functions Journal of the Egyptian Mathematical Society Convex function (α, m)-GA-convex functions Simpson type inequality
author_facet	YuJiao Li TingSong Du
author_sort	YuJiao Li
title	Some Simpson type integral inequalities for functions whose third derivatives are (α, m)- GA-convex functions
title_short	Some Simpson type integral inequalities for functions whose third derivatives are (α, m)- GA-convex functions
title_full	Some Simpson type integral inequalities for functions whose third derivatives are (α, m)- GA-convex functions
title_fullStr	Some Simpson type integral inequalities for functions whose third derivatives are (α, m)- GA-convex functions
title_full_unstemmed	Some Simpson type integral inequalities for functions whose third derivatives are (α, m)- GA-convex functions
title_sort	some simpson type integral inequalities for functions whose third derivatives are (α, m)- ga-convex functions
publisher	SpringerOpen
series	Journal of the Egyptian Mathematical Society
issn	1110-256X
publishDate	2016-04-01
description	By using power-mean integral inequality and Hölder’s integral inequality, this paper establishes some new inequalities of Simpson type for functions whose three derivatives in absolute value are the class of (α, m)-geometric-arithmetically-convex functions. Finally, some applications to special means of positive real numbers have also been presented.
topic	Convex function (α, m)-GA-convex functions Simpson type inequality
url	http://www.sciencedirect.com/science/article/pii/S1110256X15000516
work_keys_str_mv	AT yujiaoli somesimpsontypeintegralinequalitiesforfunctionswhosethirdderivativesareamgaconvexfunctions AT tingsongdu somesimpsontypeintegralinequalitiesforfunctionswhosethirdderivativesareamgaconvexfunctions
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Some Simpson type integral inequalities for functions whose third derivatives are (α, m)- GA-convex functions

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