[1] |
Al-Sa’di, S.; Bibi, M.; Seol, Y.; Muddassar, M., Milne-type fractal integral inequalities for generalized m-convex mapping, Fractals, 31, 5, 2023 · Zbl 1532.26017 · doi:10.1142/S0218348X23500810 |
[2] |
Alsina, C.; Nelsen, R. B., Means, Milne’s inequality, and quadrilateral area, Aequ. Math., 95, 4, 623-627, 2021 · Zbl 1469.26025 · doi:10.1007/s00010-021-00823-9 |
[3] |
Alzer, H.; Kovacec, A., The inequality of Milne and its converse, J. Inequal. Appl., 2002, 4, 2002 · Zbl 1004.26011 · doi:10.1155/S1025583402000292 |
[4] |
Ardila, F.; Lau, K. W.; Murty, V. N., Solution to problem 2113, Crux Math., 23, 112-114, 1997 |
[5] |
Besenyei, Á.; Dénes, P., Partial subadditivity of entropies, Linear Algebra Appl., 439, 10, 3297-3305, 2013 · Zbl 1281.94009 · doi:10.1016/j.laa.2013.03.035 |
[6] |
Bosch, P.; Carmenate, H. J.; Rodríguez, J. M.; Sigarreta, J. M., Generalized inequalities involving fractional operators of Riemann-Liouville type, AIMS Math., 7, 1, 1470-1485, 2021 · doi:10.3934/math.2022087 |
[7] |
Bosch, P.; Portilla, A.; Rodríguez, J. M.; Sigarreta, J. M., On a generalization of the Opial inequality, Demonstr. Math., 57, 2024 · Zbl 07863324 · doi:10.1515/dema-2023-0149 |
[8] |
Bosch, P.; Quintana, Y.; Rodríguez, J. M.; Sigarreta, J. M., Jensen-type inequalities for convex and m-convex functions, Open Math., 20, 946-958, 2022 · Zbl 1514.26013 · doi:10.1515/math-2022-0061 |
[9] |
Bosch, P.; Rodríguez, J. M.; Sigarreta, J. M., On new Milne-type inequalities and applications, J. Inequal. Appl., 2023, 2023 · Zbl 1532.26021 · doi:10.1186/s13660-022-02910-0 |
[10] |
Dahmani, Z., On Minkowski and Hermite-Hadamard integral inequalities via fractional integral, Ann. Funct. Anal., 1, 51-58, 2010 · Zbl 1205.26031 · doi:10.15352/afa/1399900993 |
[11] |
Davis, P. J.; Rabinowitz, P., Methods of Numerical Integration, 2007 · Zbl 1139.65016 |
[12] |
Demir, I., A new approach of Milne-type inequalities based on proportional Caputo-hybrid operator, J. Adv. App. Comput. Math., 10, 102-119, 2023 · doi:10.15377/2409-5761.2023.10.10 |
[13] |
Desta, H. D.; Budak, H.; Kara, H., New perspectives on fractional Milne-type inequalities: insights from twice-differentiable functions, Univers. J. Math. Appl., 7, 1, 30-37, 2024 · doi:10.32323/ujma.1397051 |
[14] |
Gorenflo, R.; Mainardi, F., Fractals and Fractional Calculus in Continuum Mechanics, 1997, Berlin: Springer, Berlin · Zbl 1438.26010 |
[15] |
Han, J.; Othman Mohammed, P.; Zeng, H., Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function, Open Math., 18, 794-806, 2020 · Zbl 1482.26030 · doi:10.1515/math-2020-0038 |
[16] |
Hardy, G. H.; Littlewood, J. E.; Polya, G., Inequalities, 1952, Cambridge: Cambridge university press, Cambridge · Zbl 0047.05302 |
[17] |
Iqbal, M.; Bhatti, M. I.; Nazeer, K., Generalization of inequalities analogous to Hermite-Hadamard inequality via fractional integrals, Bull. Korean Math. Soc., 52, 707-716, 2015 · Zbl 1318.26003 · doi:10.4134/BKMS.2015.52.3.707 |
[18] |
Kilbas, A. A.; Marichev, O. I.; Samko, S. G., Fractional Integrals and Derivatives. Theory and Applications, 1993, Pennsylvania: Gordon & Breach, Pennsylvania · Zbl 0818.26003 |
[19] |
Milne, E. A., Note on Rosseland’s integral for the stellar absorption, Mon. Not. R. Astron. Soc., 85, 9, 979-984, 1925 · JFM 52.1032.01 · doi:10.1093/mnras/85.9.979 |
[20] |
Nisar, K. S.; Qi, F.; Rahman, G.; Mubeen, S.; Arshad, M., Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric K-function, J. Inequal. Appl., 2018, 2018 · Zbl 1498.26032 · doi:10.1186/s13660-018-1717-8 |
[21] |
Rahman, G.; Abdeljawad, T.; Jarad, F.; Khan, A.; Sooppy Nisar, K., Certain inequalities via generalized proportional Hadamard fractional integral operators, Adv. Differ. Equ., 2019, 2019 · Zbl 1485.45015 · doi:10.1186/s13662-019-2381-0 |
[22] |
Rashid, S.; Aslam Noor, M.; Inayat Noor, K.; Chu, Y. M., Ostrowski type inequalities in the sense of generalized K-fractional integral operator for exponentially convex functions, AIMS Math., 5, 3, 2629-2645, 2020 · Zbl 1484.26038 · doi:10.3934/math.2020171 |
[23] |
Sarikaya, M. Z.; Set, E.; Özdemir, M. E., On new inequalities of Simpson’s type for s-convex functions, Comput. Math. Appl., 60, 2191-2199, 2010 · Zbl 1205.65132 · doi:10.1016/j.camwa.2010.07.033 |
[24] |
Sarikaya, M.Z., Yildirim, H.: On Milne-type inequalities and their generalizations. Bound. Value Probl. 2019(1) (2019). https://boundaryvalueproblems.springeropen.com/articles/10.1186/s13661-019-1184-4 |
[25] |
Sawano, Y.; Wadade, H., On the Gagliardo-Nirenberg type inequality in the critical Sobolev-Orrey space, J. Fourier Anal. Appl., 19, 20-47, 2013 · Zbl 1308.46049 · doi:10.1007/s00041-012-9223-8 |
[26] |
Set, E.; Tomar, M.; Sarikaya, M. Z., On generalized Grüss type inequalities for k-fractional integrals, Appl. Math. Comput., 269, 29-34, 2015 · Zbl 1410.26046 · doi:10.1016/j.amc.2015.07.026 |