<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, the authors established a new identity for differentiable functions, afterward, they obtained some new general inequalities for functions whose first derivatives in absolute value at certain powers are <italic>h</italic>-convex by using the identity. On the other hand, a general inequality is studied, which gives Hermite-Hadamard, Bullen and Simpson inequalities. Also, they gave some applications for special means for arbitrary positive numbers.</p>
</abstract>

In this paper, the authors established a new identity for differentiable functions, afterward, they obtained some new general inequalities for functions whose first derivatives in absolute value at certain powers are h-convex by using the identity. On the other hand, a general inequality is studied, which gives Hermite-Hadamard, Bullen and Simpson inequalities. Also, they gave some applications for special means for arbitrary positive numbers.

Generalizations of Hermite-Hadamard, Bullen and Simpson inequalities via <italic>h−</italic>convexity

Mustafa Kemal University, Yayladağı Vocational School

Department of Tax and Accounting, Mustafa Kemal University

Mustafa Kemal University, Faculty of Science

General Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Generalizations of Hermite-Hadamard, Bullen and Simpson inequalities via convexity

In this paper, the authors established a new identity for differentiable functions, afterward, they obtained some new general inequalities for functions whose...

Generalizations of Hermite-Hadamard, Bullen and Simpson inequalities via h−convexity

Publié en ligne: 24 nov. 2023

Pages: 77 - 95

Reçu: 20 mai 2021

Accepté: 13 juil. 2022

DOI: https://doi.org/10.2478/gm-2022-0006

Mots clés
-convex function, -convex function, Hadamard inequality, Bullen inequality, Simpson inequality, Hölder inequality

© 2022 Musa Çakmak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Generalizations of Hermite-Hadamard, Bullen and Simpson inequalities via h−convexity

Publié en ligne: 24 nov. 2023

Pages: 77 - 95

Reçu: 20 mai 2021

Accepté: 13 juil. 2022

DOI: https://doi.org/10.2478/gm-2022-0006

Mots clés-convex function, -convex function, Hadamard inequality, Bullen inequality, Simpson inequality, Hölder inequality

© 2022 Musa Çakmak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
-convex function, -convex function, Hadamard inequality, Bullen inequality, Simpson inequality, Hölder inequality