Inequalities of Hermite-Hadamard‎-Mercer Type for Convex Functions via K-Fractional Integrals

Subject Areas : International Journal of Mathematical Modelling & Computations

Muhammad Aamir Ali ¹ , Talib Hussain ² , Muhammad Zafar Iqbal ³ , Farooq Ejaz ⁴

1 - Nanjinjg University
2 - Faculty of Sciences, Department of Mathematics and Statistics, University of Agriculture Faisalabad, Pakistan
3 - Faculty of Sciences, Department of Mathematics and Statistics, University of Agriculture Faisalabad, Pakistan
4 - Faculty of Sciences, Department of Mathematics and Statistics, University of Agriculture Faisalabad, Pakistan

Received: 2020-05-17 Accepted : 2020-08-05 Published : 2020-09-01

Keywords: Hermite-Hadamard inequalities, Convex functions, Jensen-Mercer inequality, k-Riemann-Liouville fractional integrals,

Abstract :

‎In this paper‎, ‎the authors establish inequalities of the‎ Hermite-Hadamard-Mercer type for convex functions by applying k-fractional‎ integrals‎. ‎We prove some new fractional inequalities connected to the left‎ part of Hermite-Hadamard-Mercer type inequalities for differentiable‎ ‎mappings whose first derivatives in absolute value are convex‎.