Improvement of conformable fractional Hermite-Hadamard type inequality for convex functions and some new conformable fractional midpoint type inequalities
Authors :
Sercan Turhan 1 *, Imdat Iscan 2 and Mehmet Kunt 3
Author Address :
1,2 Department of Mathematics, Faculty of Sciences and Arts, Giresun University, 28200, Giresun, Turkey.
3 Department of Mathematics, Faculty of Sciences, Karadeniz Technical University, 61080, Trabzon, Turkey.
*Corresponding author.
Abstract :
In this paper, it is proved that conformable fractional Hermite-Hadamard inequality and conformable fractional Hermite-Hadamard-Fejer inequality is just the results of Hermite-Hadamard-Fej\'{e}r inequality. After this, a new conformable fractional Hermite-Hadamard inequality which is not a result of Hermite-Hadamard-Fej\'{e}r inequality and better than given in \cite{SAM16} by Set et al. is obtained. Also, new equality is proved and some new conformable fractional midpoint type inequalities are given. Our results have some relations with the results given in \cite{K04,KITK17}.
Keywords :
Convex functions, Hermite-Hadamard inequalities, Conformable fractional integrals, Midpoint type inequalities.
DOI :
Article Info :
Received : December 14, 2019; Accepted : May 19, 2020.
