On some new inequalities of Hermite–Hadamard–Mercer midpoint and trapezoidal type in q-calculus

References

[1] M. Aamir Ali, H. Budak, M. Fečkan and S. Khan, A new version of q-Hermite–Hadamard’s midpoint and trapezoid type inequalities for convex functions, Math. Slovaca 73 (2023), no. 2, 369–386. 10.1515/ms-2023-0029Suche in Google Scholar

[2] T. Abdeljawad, M. A. Ali, P. O. Mohammed and A. Kashuri, On inequalities of Hermite–Hadamard–Mercer type involving Riemann–Liouville fractional integrals, AIMS Math. 6 (2021), no. 1, 712–725. 10.3934/math.2021043Suche in Google Scholar

[3] M. A. Ali, M. Abbas, H. Budak, P. Agarwal, G. Murtaza and Y.-M. Chu, New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions, Adv. Difference Equ. 2021 (2021), Paper No. 64. 10.1186/s13662-021-03226-xSuche in Google Scholar

[4] M. A. Ali, H. Budak, Z. Zhang and H. Yildirim, Some new Simpson’s type inequalities for coordinated convex functions in quantum calculus, Math. Methods Appl. Sci. 44 (2021), no. 6, 4515–4540. 10.1002/mma.7048Suche in Google Scholar

[5] N. Alp, M. Z. Sarikaya, M. Kunt and İ. İşcan, q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci. 30 (2018), 193–203. 10.1016/j.jksus.2016.09.007Suche in Google Scholar

[6] S. Bermudo, P. Kórus and J. E. Nápoles Valdés, On q-Hermite–Hadamard inequalities for general convex functions, Acta Math. Hungar. 162 (2020), no. 1, 364–374. 10.1007/s10474-020-01025-6Suche in Google Scholar

[7] H. Budak, Some trapezoid and midpoint type inequalities for newly defined quantum integrals, Proyecciones 40 (2021), no. 1, 199–215. 10.22199/issn.0717-6279-2021-01-0013Suche in Google Scholar

[8] H. Budak, S. Erden and M. A. Ali, Simpson and Newton type inequalities for convex functions via newly defined quantum integrals, Math. Methods Appl. Sci. 44 (2021), no. 1, 378–390. 10.1002/mma.6742Suche in Google Scholar

[9] H. H. Chu, S. Rashid, Z. Hammouch and Y. M. Chu, New fractional estimates for Hermite–Hadamard–Mercer’s type inequalities, Alex. Eng. J. 59 (2020), 3079–3089. 10.1016/j.aej.2020.06.040Suche in Google Scholar

[10] S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998), no. 5, 91–95. 10.1016/S0893-9659(98)00086-XSuche in Google Scholar

[11] M. Foss and C. S. Goodrich, Partial Hölder continuity of minimizers of functionals satisfying a general asymptotic relatedness condition, J. Convex Anal. 22 (2015), no. 1, 219–246. Suche in Google Scholar

[12] H. Gauchman, Integral inequalities in q-calculus, Comput. Math. Appl. 47 (2004), no. 2–3, 281–300. 10.1016/S0898-1221(04)90025-9Suche in Google Scholar

[13] C. Goodrich and A. C. Peterson, Discrete Fractional Calculus, Springer, Cham, 2015. 10.1007/978-3-319-25562-0Suche in Google Scholar

[14] C. S. Goodrich, A topological approach to nonlocal elliptic partial differential equations on an annulus, Math. Nachr. 294 (2021), no. 2, 286–309. 10.1002/mana.201900204Suche in Google Scholar

[15] F. H. Jackson, On a q-definite integrals, Quarterly J. Pure Appl. Math. 41 (1910), 193–203. Suche in Google Scholar

[16] V. Kac and P. Cheung, Quantum Calculus, Universitext, Springer, New York, 2001. 10.1007/978-1-4613-0071-7Suche in Google Scholar

[17] M. Kian and M. S. Moslehian, Refinements of the operator Jensen–Mercer inequality, Electron. J. Linear Algebra 26 (2013), 742–753. 10.13001/1081-3810.1684Suche in Google Scholar

[18] U. S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput. 147 (2004), no. 1, 137–146. 10.1016/S0096-3003(02)00657-4Suche in Google Scholar

[19] A. M. Mercer, A variant of Jensen’s inequality, JIPAM. J. Inequal. Pure Appl. Math. 4 (2003), no. 4, Article ID 73. Suche in Google Scholar

[20] M. A. Noor, K. I. Noor and M. U. Awan, Some quantum estimates for Hermite–Hadamard inequalities, Appl. Math. Comput. 251 (2015), 675–679. 10.1016/j.amc.2014.11.090Suche in Google Scholar

[21] M. A. Noor, K. I. Noor and M. U. Awan, Some quantum integral inequalities via preinvex functions, Appl. Math. Comput. 269 (2015), 242–251. 10.1016/j.amc.2015.07.078Suche in Google Scholar

[22] H. Öğülmüş and M. Z. Sarıkaya, Hermite–Hadamard–Mercer type inequalities for fractional integrals, Filomat 35 (2021), no. 7, 2425–2436. 10.2298/FIL2107425OSuche in Google Scholar

[23] E. Set, A. O. Akdemir and E. A. Alan, Hermite–Hadamard and Hermite–Hadamard–Fejer type inequalities involving fractional integral operators, Filomat 33 (2019), no. 8, 2367–2380. 10.2298/FIL1908367SSuche in Google Scholar

[24] I. B. Sial, S. Mei, M. A. Ali and K. Nonlaopon, On some generalized Simpson’s and Newton’s inequalities for ( α , m ) -convex functions in quantum calculus, Mathematics 9 (2021), Paper No. 3266. 10.3390/math9243266Suche in Google Scholar

[25] I. B. Sial, N. Patanarapeelert, M. A. Ali, H. Budak and T. Sitthiwirattham, On some new Ostrowski–Mercer-type inequalities for differentiable functions, Axioms 11 (2022), Paper No. 132. 10.3390/axioms11030132Suche in Google Scholar

[26] T. Sitthiwirattham, M. A. Ali, A. Ali and H. Budak, A new q-Hermite–Hadamard’s inequality and estimates for midpoint type inequalities for convex functions, Miskolc Math. Notes, to appear. Suche in Google Scholar

[27] J. Soontharanon, M. A. Ali, H. Budak, K. Nonlaopon and Z. Abdullah, Simpson’s and Newton’s type inequalities for ( α , m ) -convex functions via quantum calculus, Symmetry 14 (2022), Paper No. 736. 10.3390/sym14040736Suche in Google Scholar

[28] W. Sudsutad, S. K. Ntouyas and J. Tariboon, Quantum integral inequalities for convex functions, J. Math. Inequal. 9 (2015), no. 3, 781–793. 10.7153/jmi-09-64Suche in Google Scholar

[29] J. Tariboon and S. K. Ntouyas, Quantum calculus on finite intervals and applications to impulsive difference equations, Adv. Difference Equ. 2013 (2013), Article ID 282. 10.1186/1687-1847-2013-282Suche in Google Scholar

[30] H. Wang, J. Khan, M. Adil Khan, S. Khalid and R. Khan, The Hermite–Hadamard–Jensen–Mercer type inequalities for Riemann–Liouville fractional integral, J. Math. 2021 (2021), Article ID 5516987. 10.1155/2021/5516987Suche in Google Scholar

[31] H. Zhuang, W. Liu and J. Park, Some quantum estimates of Hermite–Hadmard inequalities for quasi-convex functions, Mathematics 7 (2019), Paper No. 152. 10.3390/math7020152Suche in Google Scholar