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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528769010

Digital Object Identifier
doi:10.1515/tmj-2015-0014

Mathematical Reviews number (MathSciNet)
MR3360646

Zentralblatt MATH identifier
1318.26014

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

Keywords
Convex functions fractional integrals Hermite-Hadamard inequality means

Citation

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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