Generalizations of Hermite--Hadamard type inequalities for MT-convex functions
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Authors
Yu-Ming Chu
- School of Mathematics and Computation Science, Hunan City University, Yiyang 413000, China.
Muhammad Adil Khan
- Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan.
Tahir Ullah Khan
- Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan.
Tahir Ali
- Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan.
Abstract
In this paper, we discover two novel integral identities for twice differentiable functions. Under the utility
of these identities, we establish some generalized inequalities for classical integrals and Riemann-Liouville
fractional integrals of the Hermite-Hadamard type via functions whose derivatives absolute values are MTconvex.
At the end, we present applications for special means and several error approximations for the
trapezoidal formula.
Share and Cite
ISRP Style
Yu-Ming Chu, Muhammad Adil Khan, Tahir Ullah Khan, Tahir Ali, Generalizations of Hermite--Hadamard type inequalities for MT-convex functions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4305--4316
AMA Style
Chu Yu-Ming, Khan Muhammad Adil, Khan Tahir Ullah, Ali Tahir, Generalizations of Hermite--Hadamard type inequalities for MT-convex functions. J. Nonlinear Sci. Appl. (2016); 9(6):4305--4316
Chicago/Turabian Style
Chu, Yu-Ming, Khan, Muhammad Adil, Khan, Tahir Ullah, Ali, Tahir. "Generalizations of Hermite--Hadamard type inequalities for MT-convex functions." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4305--4316
Keywords
- MT-convex function
- Hermite-Hadamard inequality
- fractional integrals
- trapezoidal formula
- error approximation.
MSC
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