Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals

Volume 9, Issue 3, pp 766--777 http://dx.doi.org/10.22436/jnsa.009.03.05

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Authors

Wenjun Liu - College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China. Wangshu Wen - College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China. Jaekeun Park - Department of Mathematics, Hanseo University, Chungnam-do, Seosan-si 356-706, Republic of Korea.

Abstract

Some inequalities of Hermite-Hadamard type for MT-convex functions via classical integrals and Riemann- Liouville fractional integrals are introduced, respectively, and applications for special means are given. Some error estimates for the trapezoidal formula are also obtained.

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Keywords

• MT-convex function
• Hermite-Hadamard inequality
• Hölder inequality
• fractional integral
• trapezoidal formula.

MSC

•  26A33
•  33B15
•  26A51
•  26D10

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