On Upper Estimations of Hermite–Hadamard Inequalities

Yasin Kaya ()
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Yasin Kaya: Department of Mathematics, University of Dicle, 21280 Diyarbakır, Turkey

Mathematics, 2025, vol. 13, issue 21, 1-9

Abstract: Convex functions play a key role in many branches of pure and applied mathematics. In this paper, we prove that if a convex function is not continuous, then the classical Hermite–Hadamard inequality, the Hermite–Hadamard inequality for the Riemann–Liouville fractional integral and the Hermite–Hadamard inequality for the left variable order Riemann–Liouville fractional integral can be improved with slightly sharper bounds. In particular, we give new upper bounds of Hermite–Hadamard inequalities in terms of right-hand limit g a + and left-hand limit g b − values. Furthermore, classical Hermite–Hadamard inequalities only applied to closed bounded intervals, but our new improved inequalities can be applied to open bounded and half-open bounded intervals. As a consequence of our method, we also show some nonconvex functions that satisfy our new improvement of Hermite–Hadamard inequalities.

Keywords: upper estimation; convex function; Hermite–Hadamard inequality; sharp; fractional integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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