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Hermite–Hadamard type inequalities for higher-order convex functions and applications

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Abstract

In this paper, we give a new proof of the Hermite–Hadamard inequality for 3-convex functions published by Bessenyei and Páles (Publ Math Debrecen 61(3–4): 623–643, 2002) and reproved by Wąsowicz (J Math Anal Appl 332(2): 1229–1241, 2007), which is still valid under weaker conditions. Some applications to estimate the new lower and upper bounds for the sinc and hyperbolic sinc functions are given. In particular, these bounds improve or refine many recent results proposed by mathematicians.

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Acknowledgements

We would like to express our gratitude to Prof. S. Ponnusamy and the anonymous reviewers for insightful suggestions and comments which helped to improve the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Tay Nguyen University, 567 Le Duan, Buon Ma Thuot, Dak Lak, Vietnam

    Doan Thi Thuy Van & Duong Quoc Huy

  2. Tran Cao Van High School, Iahlop, Chu Se, Gia Lai, Vietnam

    Tran Minh Vu

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  1. Doan Thi Thuy Van
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  2. Tran Minh Vu
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Correspondence to Duong Quoc Huy.

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Van, D.T.T., Vu, T.M. & Huy, D.Q. Hermite–Hadamard type inequalities for higher-order convex functions and applications. J Anal 32, 869–888 (2024). https://doi.org/10.1007/s41478-023-00670-8

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