Some new q-Hermite-Hadamard type inequalities for the product of convex functions

References

• 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 with convex absolute values of second qp2-derivatives, Adv Differ Equ 2021, 7 (2021). https://doi.org/10.1186/s13662-020-03163-1.
   Google Scholar
• M. A. Ali, M. Abbas, H. Budak, P. Agarwal, G. Murtaza and Yu-Ming Chu, New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions, Adv Differ Equ 2021, 64 (2021). https://doi.org/10.1186/s13662-021-03226-x.
   Google Scholar
• M. A. Ali, Y.-M. Chu, H. Budak, A. Akkurt, and H. Yildrim, Quantum variant of Montgomery identity and Ostrowski-type inequalities for the mappings of two variables, Adv Differ Equ 2021, 25 (2021). https://doi.org/10.1186/s13662-020-03195-7.
   Google Scholar
• M. A. Ali, N. Alp, H. Budak, Y-M. Chu and Z. Zhang, On some new quantum midpoint type inequalities for twice quantum differentiable convex functions, Open Mathematics 2021, in press.
   Web of Science ®Google Scholar
• M. A. Ali, H. Budak, A. Akkurt and Y-M. Chu, Quantum Ostrowski type inequalities for twice quantum differentiable functions in quantum calculus, Open Mathematics 2021, in press.
   Web of Science ®Google Scholar
• N. Alp, M. Z. Sarikaya, M. Kunt and I. Iscan, q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, Journal of King Saud University– Science (2018) 30, 193–203. doi: 10.1016/j.jksus.2016.09.007
   Web of Science ®Google Scholar
• N. Alp and M. Z. Sarikaya, Hermite Hadamard’s type inequalities for co-ordinated convex functions on quantum integral, Applied Mathematics E-Notes, 20(2020), 341-356.
   Web of Science ®Google Scholar
• S. Bermudo, P. Kórus and J. N. Valdés, On q -Hermite–Hadamard inequalities for general convex functions, Acta Mathematica Hungarica, 1-11, 2020.
   Web of Science ®Google Scholar
• K. Brahim, R. Latifa and S. Taf, Hermite-Hadamard type inequalities for r -convex functions in q -calculus, Le Matematiche 70.2 (2015): 295-303.
   Google Scholar
• H. Budak, M. A. Ali and M. Tarhanaci, Some new q -Hermite– Hadamard like inequalities for co-ordinated convex functions. J. Optim. Theory Appl. 2020, 185, 1-16. https://doi.org/10.1007/s10957-020-01726-6.
   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, https://doi.org/10.1002/mma.6742.
   Google Scholar
• F. Chen, A note on Hermite-Hadamard inequalities for products of convex functions, Journal of Applied Mathematics, vol. 2013, Article ID 935020, 5 pages, 2013.
   Google Scholar
• S. S. Dragomir, On the Hadamard’s inequality for functions on the co-ordinates in a rectangle from the plane, Taiwanese J. Math., 5(2001), no. 4, pp. 775-788. doi: 10.11650/twjm/1500574995
   Web of Science ®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
• Y. Feng, Refining Hermite-Hadamard integral inequality by two parameters, Journal of Interdisciplinary Mathematics, 21:3, 743-746, (2018), DOI: 10.1080/09720502.2018.1424093.
   Web of Science ®Google Scholar
• V. Kac and P. Cheung Quantum calculus, Springer (2001).
   Google Scholar
• M. A. Latif, S. S. Dragomir, E. Momoniat, Some q -analogues of Hermite-Hadamard inequality of functions of two variables on finite rectangles in the plane, Journal of King Saud University-Science(2017)29,263-273. doi: 10.1016/j.jksus.2016.07.001
   Web of Science ®Google Scholar
• M. A. Latif and M. Alomari, Hadamard-type inequalities for product two convex functions on the co-ordinates, Int Math Forum. 2009;4(47):2327–2338.
   Google Scholar
• Z. Lin and J. R. Wang, New Riemann-Liouville fractional Hermite-Hadamard inequalities via two kinds of convex functions, Journal of Interdisciplinary Mathematics, 20:2, 357-382, (2017) DOI: 10.1080/09720502.2014.914281.
   Web of Science ®Google Scholar
• B. G. Pachpatte, On some inequalities for convex functions, RGMIA Res. Rep. Coll. 6 (E) (2003).
   Google Scholar
• J.E. Pečarić, F. Proschan and Y.L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
   Google Scholar
• K. Qiu and J. R. Wang, A fractional integral identity and its application to fractional Hermite-Hadamard type inequalities, Journal of Interdisciplinary Mathematics, 21:1, 1-16, (2018), DOI: 10.1080/09720502.2017.1400795.
   Web of Science ®Google Scholar
• J. Tariboon, S. K. Ntouyas, Quantum calculus on finite intervals and applications to impulsive difference equations, Adv. Difference Equ. 282 (2013) 1-19.
   Google Scholar