Korean J. Math.  Vol 28, No 4 (2020)  pp.955-971
DOI: https://doi.org/10.11568/kjm.2020.28.4.955

On some new fractional Hermite-Hadamard type inequalities for convex and co-ordinated convex functions

Muhammad AAmir Ali, Huseyin BUDAK, Sadia Sakhi


In this study, some new inequalities of Hermite-Hadamard type for convex and co-ordinated convex functions via Riemann-Liouville fractional integrals are derived. It is also shown that the results obtained in this paper are the extension of some earlier ones.


Hermite-Hadamard inequality;fractional integrals;Convex functions;co-ordinated convex functions

Subject classification



National Natural Foundation of China (No. 11971241).

Full Text:



M. A. Ali, H. Budak, M. Abbas, M. Z. Sarikaya, and A. Kashuri, Hermite- Hadamard Type Inequalities for h-convex Functions via Generalized Fractional Integrals. JOURNAL OF MATHEMATICAL EXTENSION, 14 (1) (2019). (Google Scholar)

M. A. Ali, H. Budak, Z. Zhang, and H. Yildrim, Some new Simpson’s type inequalities for co-ordinated convex functions in quantum calculus, Mathematical Methods in the Applied Sciences, https://doi.org/10.1002/mma.7048. (Google Scholar)

M. A. Ali, H. Budak, M. Abbas, and Y.-M. Chu, Quantum Hermite-Hadamard type inequalities for functions whose second qb-derivatives absolute value are convex, Advances in Difference Equation, In press, 2020. (Google Scholar)

H. Budak, Some trapezoid and midpoint type inequalities for newly defined quantum integrals, Proyecciones Journal of Mathematics, in press. (Google Scholar)

H. Budak, S. Erden, and M. A. Ali, Simpson and Newton type inequalities for convex functions via newly defined quantum integrals, Mathematical Methods in the Applied Sciences (2020). (Google Scholar)

H. Budak, M. A. Ali, and M. Tarhanaci, Some New Quantum Hermite– Hadamard-Like Inequalities for Coordinated Convex Functions, Journal of Optimization Theory and Applications (2020): 1–12. (Google Scholar)

H. Budak, M. A. Ali, and T. Tunc ̧, Quantum Ostrowski type integral inequalities for functions of two variables, Mathematical Methods in the Applied Sciences, In press, 2020. (Google Scholar)

F. Chen, A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates, Journal of Mathematical Inequalities 8 (4) (2014), 915–923. (Google Scholar)

S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000. (Google Scholar)

A. E. Farissi, Z. Latreuch and B. Belaidi, Hadamard-Type Inequalities for Twice Differentiable Functions, RGMIA Research Report collection, 12, 1 (2009), Art. 6. (Google Scholar)

A. E. Farissi, Simple proof and refinements of Hermite-Hadamard inequality, Journal of Mathematical Inequalities. 4 (3) (2010), 365–369. (Google Scholar)

R. Gorenflo, F. Mainardi, Fractional Calculus, Integral and Differential Equations of Fractional Order, Springer Verlag, Wien, 1997, 223–276. (Google Scholar)

A. Kashuri, M. A. Ali, M. Abbas, and H. Budak, New inequalities for generalized m-convex functions via generalized fractional integral operators and their applications, International Journal of Nonlinear Analysis and Applications 10 (2) (2019), 275–299. (Google Scholar)

A. Kashuri, M. A. Ali, M. Abbas, H. Budak, and M. Z. Sarikaya, Fractional integral inequalities for generalized convexity, Tbilisi Mathematical Journal 13 (3) (2020), 63–83. (Google Scholar)

̈ (Google Scholar)

M. E. Ozdemir, S ̧. Yildiz and A. O. Akdemir, On some new Hadamard-type inequalities for co-ordinated quasi-convex functions, Hacettepe Journal of Mathematics and Statistics 41 (5) (2012), 697–707. (Google Scholar)

J.E. Peˇcari ́c, F. Proschan and Y.L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992. (Google Scholar)

M. Z. Sarikaya, On the Hermite-Hadamard-type inequalities for co-ordinated convex functions via fractional integrals, Integral Transforms and Special Functions 25 (2) (2014), 134–147. (Google Scholar)

M. Z. Sarikaya, E. Set, H. Yildiz and N. Ba ̧sak, Hermite-Hadamard’s inequalities for fractional integrals and related inequalities, Mathematical and Computer Modelling 57 (2013), 2403–2407. (Google Scholar)


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