$Extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integrals$

Extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integrals

Abstract The authors discover a general k-fractional integral identity with multi-parameters for twice differentiable functions. By using this integral equation, the authors derive some new bounds on Hermite–Hadamard’s and Simpson’s inequalities for generalized (m,h) $(m,h)$-preinvex functions throu...

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Main Authors:	Yao Zhang, Ting-Song Du, Hao Wang, Yan-Jun Shen, Artion Kashuri
Format:	Article
Language:	English
Published:	SpringerOpen 2018-02-01
Series:	Journal of Inequalities and Applications
Subjects:	Hermite–Hadamard’s inequality Simpson’s inequality Generalized ( m , h ) $(m,h)$ -preinvex functions k-fractional integrals
Online Access:	http://link.springer.com/article/10.1186/s13660-018-1639-5

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spelling	doaj-36f879a938d54b18a2a6d68922a6bcd72020-11-25T00:45:59ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-02-012018113010.1186/s13660-018-1639-5Extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integralsYao Zhang0Ting-Song Du1Hao Wang2Yan-Jun Shen3Artion Kashuri4Department of Mathematics, College of Science, China Three Gorges UniversityDepartment of Mathematics, College of Science, China Three Gorges UniversityDepartment of Mathematics, College of Science, China Three Gorges UniversityHubei Provincial Collaborative Innovation Center for New Energy Microgrid, China Three Gorges UniversityDepartment of Mathematics, Faculty of Technical Science, University “Ismail Qemali”Abstract The authors discover a general k-fractional integral identity with multi-parameters for twice differentiable functions. By using this integral equation, the authors derive some new bounds on Hermite–Hadamard’s and Simpson’s inequalities for generalized (m,h) $(m,h)$-preinvex functions through k-fractional integrals. By taking the special parameter values for various suitable choices of function h, some interesting results are also obtained.http://link.springer.com/article/10.1186/s13660-018-1639-5Hermite–Hadamard’s inequalitySimpson’s inequalityGeneralized ( m , h ) $(m,h)$ -preinvex functionsk-fractional integrals
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yao Zhang Ting-Song Du Hao Wang Yan-Jun Shen Artion Kashuri
spellingShingle	Yao Zhang Ting-Song Du Hao Wang Yan-Jun Shen Artion Kashuri Extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integrals Journal of Inequalities and Applications Hermite–Hadamard’s inequality Simpson’s inequality Generalized ( m , h ) $(m,h)$ -preinvex functions k-fractional integrals
author_facet	Yao Zhang Ting-Song Du Hao Wang Yan-Jun Shen Artion Kashuri
author_sort	Yao Zhang
title	Extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integrals
title_short	Extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integrals
title_full	Extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integrals
title_fullStr	Extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integrals
title_full_unstemmed	Extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integrals
title_sort	extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integrals
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2018-02-01
description	Abstract The authors discover a general k-fractional integral identity with multi-parameters for twice differentiable functions. By using this integral equation, the authors derive some new bounds on Hermite–Hadamard’s and Simpson’s inequalities for generalized (m,h) $(m,h)$-preinvex functions through k-fractional integrals. By taking the special parameter values for various suitable choices of function h, some interesting results are also obtained.
topic	Hermite–Hadamard’s inequality Simpson’s inequality Generalized ( m , h ) $(m,h)$ -preinvex functions k-fractional integrals
url	http://link.springer.com/article/10.1186/s13660-018-1639-5
work_keys_str_mv	AT yaozhang extensionsofdifferenttypeparameterizedinequalitiesforgeneralizedmhmhpreinvexmappingsviakfractionalintegrals AT tingsongdu extensionsofdifferenttypeparameterizedinequalitiesforgeneralizedmhmhpreinvexmappingsviakfractionalintegrals AT haowang extensionsofdifferenttypeparameterizedinequalitiesforgeneralizedmhmhpreinvexmappingsviakfractionalintegrals AT yanjunshen extensionsofdifferenttypeparameterizedinequalitiesforgeneralizedmhmhpreinvexmappingsviakfractionalintegrals AT artionkashuri extensionsofdifferenttypeparameterizedinequalitiesforgeneralizedmhmhpreinvexmappingsviakfractionalintegrals
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Extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integrals

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