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Malik, Sumaiya; Khan, Khuram Ali; Nosheen, Ammara; Awan, Khalid Mahmood

Generalization of Montgomery identity via Taylor formula on time scales. (English) Zbl 1506.26035

J. Inequal. Appl. 2022, Paper No. 24, 17 p. (2022).

MSC:

26D15 Inequalities for sums, series and integrals
26A33 Fractional derivatives and integrals
26A51 Convexity of real functions in one variable, generalizations
26E70 Real analysis on time scales or measure chains
39B62 Functional inequalities, including subadditivity, convexity, etc.

Keywords:

Montgomery identity; Ostrowski inequality; trapezoid inequality; time scales calculus
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References:

[1] Adil Khan, M.; Khan, S.; Ullah, I.; Ali Khan, K.; Chu, Y. M., A novel approach to the Jensen gap through Taylor���s theorem, Math. Methods Appl. Sci., 44, 5, 3324-3333 (2021) · Zbl 1472.26009 · doi:10.1002/mma.6944
[2] Akin, E., Cauchy functions for dynamic equations on a measure chain, J. Math. Anal. Appl., 267, 1, 97-115 (2002) · Zbl 1006.39015 · doi:10.1006/jmaa.2001.7753
[3] Ali, M. A.; Chu, Y. M.; Budak, H.; Akkurt, A.; Yaldrim, H.; Zahid, M. A., Quantum variant of Montgomery identity and Ostrowski-type inequalities for the mappings of two variables, Adv. Differ. Equ., 2021, 1 (2021) · doi:10.1186/s13662-020-03162-2
[4] Aljinović, A. A.; Pečaríc, J.; Vukelíc, A., On some Ostrowski type inequalities via Montgomery identity and Taylor’s formula II, Tamkang J. Math., 36, 4, 279-301 (2005) · Zbl 1094.26015 · doi:10.5556/j.tkjm.36.2005.100
[5] Alshanti, W.G.: Inequality of Ostrowski type for mappings with bounded fourth order partial derivatives. Abstr. Appl. Anal. 2019 (2019) · Zbl 1474.26076
[6] Baleanu, D.; Mohammed, P. O.; Zeng, S., Inequalities of trapezoidal type involving generalized fractional integrals, Alex. Eng. J., 59, 5, 2975-2984 (2020) · doi:10.1016/j.aej.2020.03.039
[7] Bohner, M.; Georgiev, S. G., Multivariable Dynamic Calculus on Time Scales (2016), Switzerland: Springer, Switzerland · Zbl 1475.26001 · doi:10.1007/978-3-319-47620-9
[8] Bohner, M.; Matthews, T., Ostrowski inequalities on time scales, J. Inequal. Pure Appl. Math., 9, 1, 8 (2008) · Zbl 1178.26020
[9] Bohner, M.; Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (2001), Boston: Birkhäuser, Boston · Zbl 0978.39001 · doi:10.1007/978-1-4612-0201-1
[10] Bohner, M.; Peterson, A., Advances in Dynamic Equations on Time Scales: An Introduction with Applications (2003), Boston: Birkhäuser, Boston · Zbl 1025.34001 · doi:10.1007/978-0-8176-8230-9
[11] Butt, S. I.; Khan, K. A.; Pečarić, J., Generalization of Popoviciu inequality for higher order convex function via Tayor’s polynomial, Acta Univ. Apulensis, Mat.-Inform., 42, 181-200 (2015) · Zbl 1374.26037
[12] Erden, S.; Çelik, N.; Khan, M. A., Refined inequalities of perturbed Ostrowski type for higher-order absolutely continuous functions and applications, AIMS Math., 6, 1, 389-404 (2021) · Zbl 1484.44001 · doi:10.3934/math.2021023
[13] Karpuz, B., Unbounded oscillation of higher-order nonlinear delay dynamic equations of neutral type with oscillating coefficients, Electron. J. Qual. Theory Differ. Equ., 2009 (2009) · Zbl 1184.34072
[14] Khan, K. A.; Awan, K. M.; Malik, S.; Nosheen, A., Extension of Montgomery identity via Taylor polynomial on time scales, Turk. J. Math., 44, 5, 1708-1723 (2020) · Zbl 1506.26016 · doi:10.3906/mat-1906-11
[15] Khan, M. A.; Khurshid, Y.; Chu, Y. M., Hermite-Hadamard type inequalities via the Montgomery identity, Commun. Math. Appl., 10, 1, 85-97 (2019)
[16] Kunt, M.; Kashuri, A.; Du, T.; Baidar, A. W., Quantum Montgomery identity and quantum estimates of Ostrowski type inequalities, AIMS Math., 5, 6, 5439-5457 (2020) · Zbl 1484.26076 · doi:10.3934/math.2020349
[17] Mehmood, N.; Agarwal, R. P.; Butt, S. I.; Pecaric, J., New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity, J. Inequal. Appl., 2017 (2017) · Zbl 1362.26023 · doi:10.1186/s13660-017-1379-y
[18] Mitrinovic, D. S.; Pečaríc, J. E.; Fink, A. M., Inequalities Involving Functions and Their Integrals and Derivatives (1991), Berlin: Springer, Berlin · Zbl 0744.26011 · doi:10.1007/978-94-011-3562-7
[19] Neang, P.; Nonlaopon, K.; Tariboon, J.; Ntouyas, S. K.; Agarwal, P., Some trapezoid and midpoint type inequalities via fractional (p,q)-calculus, Adv. Differ. Equ., 2021, 1 (2021) · Zbl 1494.26028 · doi:10.1186/s13662-021-03487-6
[20] Pečarić, J., On the Čebyšev inequality, Bul. Inst. Politehn. Timisoara, 25, 39, 10-11 (1980) · Zbl 0478.26009
[21] Sarikaya, M. Z.; Aktan, N.; Yildirim, H., On weighted C̆ebys̆ev-Grüss inequalities on time scales, J. Math. Inequal., 2, 2, 185-195 (2008) · Zbl 1152.26326 · doi:10.7153/jmi-02-17
[22] You, X.; Farid, G.; Maheen, K., Fractional Ostrowski type inequalities via generalized Mittag-Leffler function, Mathematical Problems in Engineering 2020 (2020) · Zbl 1459.26041
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