Simpson’s Integral Inequalities for Twice Differentiable Convex Functions

Simpson’s Integral Inequalities for Twice Differentiable Convex Functions

Integral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In the present research article, we obtain new inequalities of Simpson’s integral type based on the φ-convex and φ-quasiconvex functions in the seco...

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Main Authors: Miguel Vivas-Cortez, Thabet Abdeljawad, Pshtiwan Othman Mohammed, Yenny Rangel-Oliveros
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2020/1936461
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spelling doaj-09f6a1f4d39540ce9e02047d0a4cb7302020-11-25T03:36:33ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/19364611936461Simpson’s Integral Inequalities for Twice Differentiable Convex FunctionsMiguel Vivas-Cortez0Thabet Abdeljawad1Pshtiwan Othman Mohammed2Yenny Rangel-Oliveros3Facultad de Ciencias Exactas y Naturales, Escuela de Ciencias Fisicas y Matematica, Pontificia Universidad Católica Del Ecuador, Quito, EcuadorDepartment of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaDepartment of Mathematics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, IraqFacultad de Ciencias Exactas y Naturales, Escuela de Ciencias Fisicas y Matematica, Pontificia Universidad Católica Del Ecuador, Quito, EcuadorIntegral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In the present research article, we obtain new inequalities of Simpson’s integral type based on the φ-convex and φ-quasiconvex functions in the second derivative sense. In the last sections, some applications on special functions are provided and shown via two figures to demonstrate the explanation of the readers.http://dx.doi.org/10.1155/2020/1936461
collection DOAJ
language English
format Article
sources DOAJ
author Miguel Vivas-Cortez
Thabet Abdeljawad
Pshtiwan Othman Mohammed
Yenny Rangel-Oliveros
spellingShingle Miguel Vivas-Cortez
Thabet Abdeljawad
Pshtiwan Othman Mohammed
Yenny Rangel-Oliveros
Simpson’s Integral Inequalities for Twice Differentiable Convex Functions
Mathematical Problems in Engineering
author_facet Miguel Vivas-Cortez
Thabet Abdeljawad
Pshtiwan Othman Mohammed
Yenny Rangel-Oliveros
author_sort Miguel Vivas-Cortez
title Simpson’s Integral Inequalities for Twice Differentiable Convex Functions
title_short Simpson’s Integral Inequalities for Twice Differentiable Convex Functions
title_full Simpson’s Integral Inequalities for Twice Differentiable Convex Functions
title_fullStr Simpson’s Integral Inequalities for Twice Differentiable Convex Functions
title_full_unstemmed Simpson’s Integral Inequalities for Twice Differentiable Convex Functions
title_sort simpson’s integral inequalities for twice differentiable convex functions
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2020-01-01
description Integral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In the present research article, we obtain new inequalities of Simpson’s integral type based on the φ-convex and φ-quasiconvex functions in the second derivative sense. In the last sections, some applications on special functions are provided and shown via two figures to demonstrate the explanation of the readers.
url http://dx.doi.org/10.1155/2020/1936461
work_keys_str_mv AT miguelvivascortez simpsonsintegralinequalitiesfortwicedifferentiableconvexfunctions
AT thabetabdeljawad simpsonsintegralinequalitiesfortwicedifferentiableconvexfunctions
AT pshtiwanothmanmohammed simpsonsintegralinequalitiesfortwicedifferentiableconvexfunctions
AT yennyrangeloliveros simpsonsintegralinequalitiesfortwicedifferentiableconvexfunctions
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