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Ni, Jinbo; Chen, Gang; Dong, Hudie

Study on Hermite-Hadamard-type inequalities using a new generalized fractional integral operator. (English) Zbl 1532.26033

J. Inequal. Appl. 2023, Paper No. 59, 17 p. (2023).

Cited in 1 Document

MSC:

26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations
26A33 Fractional derivatives and integrals
26D10 Inequalities involving derivatives and differential and integral operators

Keywords:

fractional integral operator; Hermite-Hadamard-type inequality; convex function
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References:

[1] Peajcariaac, J. E.; Tong, Y. L., Convex Functions, Partial Orderings, and Statistical Applications (1992), San Diego: Academic Press, San Diego · Zbl 0749.26004
[2] Hadamard, J., Etude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par Riemann, J. Math. Pures Appl., 58, 171-216 (1893) · JFM 25.0698.03
[3] Dragomir, S. S., Hermite-Hadamard’s type inequalities for operator convex functions, Appl. Math. Comput., 218, 3, 766-772 (2011) · Zbl 1239.47009
[4] Wang, J. R.; Zhu, C.; Zhou, Y., New generalized Hermite-Hadamard type inequalities and applications to special means, J. Inequal. Appl., 2013, 1 (2013) · Zbl 1285.26014 · doi:10.1186/1029-242X-2013-325
[5] Awan, M. U.; Noor, M. A.; Safdar, F., Hermite-Hadamard type inequalities with applications, Miskolc Math. Notes, 21, 2, 593-614 (2020) · Zbl 1474.26080 · doi:10.18514/MMN.2020.2837
[6] Budak, H.; Khan, S.; Ali, M. A., Refinements of quantum Hermite-Hadamard-type inequalities, Open Math., 19, 1, 724-734 (2021) · Zbl 1481.26016 · doi:10.1515/math-2021-0029
[7] Sarikaya, M. Z., On new Hermite Hadamard Fejér type integral inequalities, Stud. Univ. Babeş-Bolyai, Math., 57, 3, 377-386 (2012) · Zbl 1289.26054
[8] Awan, M. U.; Talib, S.; Kashuri, A., Some new (p,q)-Dragomir-Agarwal and Iyengar type integral inequalities and their applications, AIMS Math., 7, 4, 5728-5751 (2022) · doi:10.3934/math.2022317
[9] Du, L.; Xu, R., Some new Pachpatte type inequalities on time scales and their applications, J. Math. Inequal., 6, 2, 229-240 (2012) · Zbl 1259.34092 · doi:10.7153/jmi-06-23
[10] Kilbas, A. A.; Marichev, O. I.; Samko, S. G., Fractional Integrals and Derivatives. Theory and Applications (1993), Switzerland: Gordon and Breach, Switzerland · Zbl 0818.26003
[11] Sarikaya, M. Z.; Set, E.; Yaldiz, H., Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model., 57, 10, 2403-2407 (2013) · Zbl 1286.26018 · doi:10.1016/j.mcm.2011.12.048
[12] Sarikaya, M. Z.; Yaldiz, H., On generalized Hermite-Hadamard type integral inequalities involving Riemann-Liouville fractional integrals, Nihonkai Math. J., 25, 2, 93-104 (2014) · Zbl 1312.26034
[13] Agarwal, P.; Jleli, M.; Tomar, M., Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals, J. Inequal. Appl., 2017, 1 (2017) · Zbl 1359.26005 · doi:10.1186/s13660-017-1318-y
[14] Awan, M. U.; Noor, M. A.; Mihai, M. V., Inequalities via harmonic convex functions: conformable fractional calculus approach, J. Math. Inequal., 12, 1, 143-153 (2018) · Zbl 1391.26046 · doi:10.7153/jmi-2018-12-11
[15] Zhao, Y.; Sang, H.; Xiong, W., Hermite-Hadamard-type inequalities involving ψ-Riemann-Liouville fractional integrals via s-convex functions, J. Inequal. Appl., 2020, 1 (2020) · Zbl 1503.26086 · doi:10.1186/s13660-020-02389-7
[16] Set, E.; Akdemir, A. O.; Karaoǧlan, A., On new generalizations of Hermite-Hadamard type inequalities via Atangana-Baleanu fractional integral operators, Axioms, 10, 3, 1-13 (2021) · doi:10.3390/axioms10030223
[17] Sahoo, S. K.; Jarad, F.; Kodamasingh, B., Hermite-Hadamard type inclusions via generalized Atangana-Baleanu fractional operator with application, AIMS Math., 7, 7, 12303-12321 (2022) · doi:10.3934/math.2022683
[18] Mehreen, N.; Anwar, M., Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for p-convex functions via conformable fractional integrals, J. Inequal. Appl., 2020, 1 (2020) · Zbl 1503.26066 · doi:10.1186/s13660-020-02363-3
[19] Noor, M. A.; Noor, K. I.; Awan, M. U., Generalized fractional Hermite-Hadamard inequalities, Miskolc Math. Notes, 21, 2, 1001-1011 (2020) · Zbl 1474.26026 · doi:10.18514/MMN.2020.1143
[20] Ali, M. A.; Sarikaya, M. Z.; Budak, H., Fractional Hermite-Hadamard type inequalities for subadditive functions, Filomat, 36, 11, 3715-3729 (2022) · doi:10.2298/FIL2211715A
[21] Aljaaidi, T. A.; Pachpatte, D. B., Reverse Hermite-Hadamard’s inequalities using ψ-fractional integral, Eng. App. Sci. Lett., 3, 4, 75-84 (2020) · doi:10.30538/psrp-easl2020.0053
[22] Set, E.; Choi, J.; Celik, B., Certain Hermite-Hadamard type inequalities involving generalized fractional integral operators, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., 112, 4, 1539-1547 (2018) · Zbl 1400.26062 · doi:10.1007/s13398-017-0444-1
[23] Ahmad, B.; Alsaedi, A.; Kirane, M., Hermite-Hadamard, Hermite-Hadamard-Fejér, Dragomir-Agarwal and Pachpatte type inequalities for convex functions via new fractional integrals, J. Comput. Appl. Math., 353, 2019, 120-129 (2019) · Zbl 1426.26008 · doi:10.1016/j.cam.2018.12.030
[24] Aljaaidi, T. A.; Pachpatte, D. B.; Abdeljawad, T., Generalized proportional fractional integral Hermite-Hadamard’s inequalities, Adv. Differ. Equ., 2021, 1 (2021) · Zbl 1494.26032 · doi:10.1186/s13662-021-03651-y
[25] Jleli, M.; Samet, B., On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function, J. Nonlinear Sci. Appl., 9, 3, 1252-1260 (2016) · Zbl 1329.26036 · doi:10.22436/jnsa.009.03.50
[26] Budak, H., On Fejér type inequalities for convex mappings utilizing fractional integrals of a function with respect to another function, Results Math., 74, 1, 1-15 (2019) · Zbl 1407.26017 · doi:10.1007/s00025-019-0960-8
[27] Sarikaya, M. Z.; Ertugral, F., On the generalized Hermite-Hadamard inequalities, An. Univ. Craiova, Ser. Mat. Inform., 47, 1, 193-213 (2020) · Zbl 1488.26138
[28] Kashuri, A.; Liko, R., On Fejér type inequalities for convex mappings utilizing generalized fractional integrals, Appl. Appl. Math., 15, 1, 240-255 (2020) · Zbl 1444.26033
[29] Iscan, I., Hermite-Hadamard-Fejér type inequalities for convex functions via fractional integrals, Stud. Univ. Babeş-Bolyai, Math., 60, 3, 355-366 (2015) · Zbl 1374.26041
[30] Mubeen, S.; Habibullah, G. M., k-Fractional integrals and application, Int. J. Contemp. Math. Sci., 7, 2, 89-94 (2012) · Zbl 1248.33005
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