Next Article in Journal
Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function
Previous Article in Journal
Viscosity Methods and Split Common Fixed Point Problems for Demicontractive Mappings
Previous Article in Special Issue
Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications
Open AccessFeature PaperArticle

Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel

by 1, 2,3,* and 1
1
School of Mathematics and Finance, Xiangnan University, Chenzhou 411105, China
2
Department of Mathematics, Guizhou University, Guiyang 550025, China
3
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(9), 845; https://doi.org/10.3390/math7090845
Received: 24 August 2019 / Revised: 8 September 2019 / Accepted: 9 September 2019 / Published: 12 September 2019
In this paper, we establish three fundamental integral identities by the first- and second-order derivatives for a given function via the fractional integrals with exponential kernel. With the help of these new fractional integral identities, we introduce a few interesting Hermite–Hadamard-type inequalities involving left-sided and right-sided fractional integrals with exponential kernels for convex functions. Finally, some applications to special means of real number are presented.
Keywords: convex functions, Hermite–Hadamard-type inequalities, fractional integrals, exponential kernel. convex functions, Hermite–Hadamard-type inequalities, fractional integrals, exponential kernel.
MDPI and ACS Style

Wu, X.; Wang, J.; Zhang, A.J. Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel . Mathematics 2019, 7, 845.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map

1
Back to TopTop