Some new integral inequalities of the Simpson type for MT-convex functions
Keywords:
integral inequality, MT-convex function, integral identity, SimpsonAbstract
In the paper, with the aid of a known integral identity, the authors establish some new inequalities, similar to the celebrated Simpson's integral inequality, for differentiable MT-convex functions.
References
R.-F. Bai, F. Qi, and B.-Y. Xi, Hermite-Hadamard type inequalities for the m- and (α,m)-logarithmically convex functions, Filomat 27 (2013), no. 1, 1-7; available online at https://doi.org/10.2298/FIL1301001B.
S.-P. Bai, S.-H. Wang, and F. Qi, On HT-convexity and Hadamard-type inequalities, J. Inequal. Appl. 2020, Paper No. 3, 12 pages; available online at https://doi.org/10.1186/s13660-019-2276-3.
J. Cao, H.M. Srivastava, and Z.-G. Liu, Some iterated fractional q-integrals and their applications, Fract. Calc. Appl. Anal. 21 (2018), no. 3, 672-695; available online at https://doi.org/10.1515/fca-2018-0036.
Y.-M. Chu, M.A. Khan, T.U. Khan, and T. Ali, Generalizations of Hermite-Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl. 9 (2016), no. 6, 4305-4316; available online at https://doi.org/10.22436/jnsa.009. 06.72.
U.N. Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl. 6 (2014), no. 4, 1?15; available online at https://doi.org/10.1007/BF01837981.
W. Liu and W. Wen, Some generalizations of different type of integral inequalities for MT-convex functions, Filomat 30 (2016), no. 2, 333-342; available online at https://doi.org/10.2298/FIL1602333L.
W. Liu, W. Wen, and J. Park, Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals, J. Nonlinear Sci. Appl. 9 (2016), no. 3, 766-777; available online at https://doi.org/10.22436/jnsa. 009.03.05.
W. Liu, W. Wen, and J. Park, Ostrowski type fractional integral inequalities for MT-convex functions, Miskolc Math. Notes 16 (2015), no. 1, 249-256; available online at https://doi.org/10.18514/mmn.2015.1131.
P.O. Mohammed, Some new Hermite-Hadamard type inequalities for MT-convex functions on differentiable coordinates, J. King Saud Univ. Sci. 30 (2018), no. 2, 258-262; available online at https://doi.org/10.1016/j.jksus.2017.07.011.
J. Park, Hermite?Hadamard-like type inequalities for twice differentiable MT-Convex functions, Appl. Math. Sci. 9 (2015), no. 105, 5235-5250; available online at https://doi.org/10.12988/ams.2015.56460.
F. Qi, C.-P. Chen, and D. Lim, Several identities containing central binomial coefficients and derived from series expansions of powers of the arcsine function, Results Nonlinear Anal. 4 (2021), no. 1, 57-64; available online at https://doi.org/ 10.53006/rna.867047.
F. Qi and A. Wan, Geometric interpretations and reversed versions of Young's integral inequality, Adv. Theory Nonlinear Anal. Appl. 5 (2021), no. 1, 1-6; available online at https://doi.org/10.31197/atnaa.817804.
M. Tunç and H. Yildirim, On MT-convexity, arXiv (2012), available online at https:///arxiv.org/pdf/1205.5453.
