On <i>q</i>-Hermite-Hadamard Inequalities for Differentiable Convex Functions

On <i>q</i>-Hermite-Hadamard Inequalities for Differentiable Convex Functions

In this paper, we establish some new results on the left-hand side of the <i>q</i>-Hermite&#8722;Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (<i>q</i>-Hermite Hadamard inequalities and quantum e...

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Bibliographic Details
Main Authors: Seksan Jhanthanam, Jessada Tariboon, Sotiris K. Ntouyas, Kamsing Nonlaopon
Format: Article
Language:English
Published: MDPI AG 2019-07-01
Series:Mathematics
Subjects:
Hermite-Hadamard inequalities
<i>q</i>-derivative
<i>q</i>-integral
convex functions
Online Access:https://www.mdpi.com/2227-7390/7/7/632
Description
Summary:In this paper, we establish some new results on the left-hand side of the <i>q</i>-Hermite&#8722;Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (<i>q</i>-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 2018, 30, 193-203), by considering the critical point-type inequalities.
ISSN:2227-7390

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