Tbilisi Mathematical Journal

Fractional Hermite-Hadmard inequalities for convex functions and applications

Muhammad Aslam Noor, Khalida Inayat Noor, and Muhammad Uzair Awan

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In this paper, we derive a new lemma including third-order derivative of a function via fractional integrals. Using this lemma, we establish some new fractional estimates for Hermite-Hadamard type inequalities for convex functions. Several special cases are also discussed. Some applications to special means of real numbers are also discussed. The ideas and techniques used in this paper may stimulate future investigations regarding Hermite-Hadamard type of inequalities and its application in different areas.

Article information

Tbilisi Math. J., Volume 8, Issue 2 (2015), 103-113.

Received: 14 December 2014
Accepted: 22 May 2015
First available in Project Euclid: 12 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A33: Fractional derivatives and integrals
Secondary: 26D15: Inequalities for sums, series and integrals 26A51: Convexity, generalizations

Convex functions fractional integrals Hermite-Hadamard inequality means


Noor, Muhammad Aslam; Noor, Khalida Inayat; Awan, Muhammad Uzair. Fractional Hermite-Hadmard inequalities for convex functions and applications. Tbilisi Math. J. 8 (2015), no. 2, 103--113. doi:10.1515/tmj-2015-0014. https://projecteuclid.org/euclid.tbilisi/1528769010

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