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The Principle of Differential Subordination and Its Application to Analytic and p-Valent Functions Defined by a Generalized Fractional Differintegral Operator
Open AccessArticle

Some Improvements of the Hermite–Hadamard Integral Inequality

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Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam
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Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam
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Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
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Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 117; https://doi.org/10.3390/sym12010117
Received: 9 December 2019 / Revised: 25 December 2019 / Accepted: 2 January 2020 / Published: 7 January 2020
(This article belongs to the Special Issue Integral Transformations, Operational Calculus and Their Applications)
We propose several improvements of the Hermite–Hadamard inequality in the form of linear combination of its end-points and establish best possible constants. Improvements of a second order for the class Φ ( I ) with applications in Analysis and Theory of Means are also given. View Full-Text
Keywords: Convex function; Simpson’s rule; differentiable function Convex function; Simpson’s rule; differentiable function
MDPI and ACS Style

Simić, S.; Bin-Mohsin, B. Some Improvements of the Hermite–Hadamard Integral Inequality. Symmetry 2020, 12, 117.

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