Generalized perturbed Ostrowski-type inequalities

Martin Bohner, Asif Khan, Maria Khan, Faraz Mehmood, Muhammad Awais Shaikh

Abstract


In this paper, we present new perturbed inequalities of Ostrowski-type, for twice differentiable functions with absolutely continuous first derivative and second-order derivative in some \(L^p\)-space for \(1\leq p\leq \infty\).

Keywords


Ostrowski’s inequality; perturbed inequality; twice differentiable

Full Text:

PDF

References


Anastassiou, G. A., Multivariate Ostrowski type inequalities, Acta Math. Hungar. 76 (4) (1997), 267–278.

Anastassiou, G. A., Complex multivariate Fink type identity applied to complex multivariate Ostrowski and Gruss inequalities, Indian J. Math. 61 (2) (2019), 199–237.

Barnett, N. S., Cerone, P., Dragomir, S. S., Roumeliotis, J., Sofo, A., A survey on Ostrowski type inequalities for twice differentiable mappings and applications, in: Inequality theory and applications. Vol. I, Nova Sci. Publ., Huntington, NY, 2001, 33–85.

Bohner, M., Matthews, T., Ostrowski inequalities on time scales, JIPAM. J. Inequal. Pure Appl. Math. 9 (1) (2008), Art. 6, 8 pp.

Bohner, M., Matthews, T., and Tuna, A., Weighted Ostrowski–Gruss inequalities on time scales, Afr. Diaspora J. Math. 12 (1) (2011), 89–99.

Cerone, P., Dragomir, S. S., Trapezoidal-type rules from an inequalities point of view, in: Handbook of analytic-computational methods in applied mathematics, Chapman & Hall/CRC, Boca Raton, FL, 2000, 65–134.

Cerone, P., Dragomir, S. S., and Roumeliotis, J., An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, East Asian Math. J. 15 (1) (1999), 1–9.

Cerone, P., Dragomir, S. S., and Roumeliotis, J., An inequality of Ostrowski type for mappings whose second derivatives belong to L1(a; b) and applications, Honam Math. J. 21 (1) (1999), 127–137.

Cerone, P., Dragomir, S. S., and Roumeliotis, J., An Ostrowski type inequality for mappings whose second derivatives belong to Lp(a, b) and applications, J. Indian Math. Soc. (N.S.) 67 (1–4) (2000), 59–67.

Cheng, X.-L., Improvement of some Ostrowski–Gruss type inequalities, Comput. Math. Appl. 42 (1–2) (2001), 109–114.

Dragomir, S. S., Sofo, A., An integral inequality for twice differentiable mappings and applications, Tamkang J. Math. 31 (4) (2000), 257–266.

Dragomir, S. S., Wang, S., An inequality of Ostrowski–Gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl. 33 (11) (1997), 15–20.

Erden, S., Budak, H., Sarikaya, M. Z., Iftikhar, S., and Kumam, P., Fractional Ostrowski type inequalities for bounded functions, J. Inequal. Appl. 2020, Paper No. 123, 11 pp.

Kermausuor S., A generalization of Ostrowski’s inequality for functions of bounded variation via a parameter, Aust. J. Math. Anal. Appl. 16 (1) (2019), Art. 16, 12 pp.

Kermausuor, S., Generalized Ostrowski-type inequalities involving second derivatives via the Katugampola fractional integrals, J. Nonlinear Sci. Appl. 12 (8) (2019), 509–522.

Kermausuor, S., Nwaeze, E. R., New generalized 2D Ostrowski type inequalities on time scales with (k^2) points using a parameter. Filomat 32 (9) (2018), 3155–3169.

Kermausuor, S., Nwaeze, E. R., New Ostrowski and Ostrowski–Gruss type inequalities for double integrals on time scales involving a combination of (Delta)-integral means, Tamkang J. Math. 49 (4) (2018), 277–289.

Kvesic, L., Pecaric, J., and Ribicic Penava, M., Generalizations of Ostrowski type inequalities via Hermite polynomials, J. Inequal. Appl. 2020, Paper No. 176, 14 pp.

Liu, Z., Some Ostrowski type inequalities, Math. Comput. Modelling 48 (5–6) (2008), 949–960.

Masjed-Jamei, M., Dragomir, S. S., A generalization of the Ostrowski–Gruss inequality, Anal. Appl. (Singap.) 12 (2) (2014), 117–130.

Matic, M., Pecaric, J., and Ujevic, N., Improvement and further generalization of inequalities of Ostrowski–Gruss type, Comput. Math. Appl. 39 (3–4) (2000), 161–175.

Milovanovic, G. V., Pecaric, J. E., On generalization of the inequality of A. Ostrowski and some related applications, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. (544–576) (1976), 155–158.

Nwaeze, E., R., Kaplan, N., Gozde Tuna, F., and Tuna, A., Some new inequalities of the Ostrowski–Gruss, Cebysev, and trapezoid types on time scales. J. Nonlinear Sci. Appl. 12 (4) (2019), 192–205.

Nwaeze, E., R., Kermausuor, S., Generalization of Ostrowski kind inequality for double integrals on time scales, J. Inequal. Spec. Funct. 10 (4) (2019), 35–50.

Ostrowski, A., Uber die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv. 10 (1) (1937), 226–227.

Pachpatte, D. B., Some Ostrowski type inequalities for double integrals on time scales, Acta Appl. Math. 161 (2019), 1–11.

Rafiq, A., Mir, N. A., An Ostrowski type inequality for p-norms, JIPAM. J. Inequal. Pure Appl. Math. 7 (3) (2006), Art. 112, 7 pp.

Ujevic, N., A generalization of Ostrowski’s inequality and applications in numerical integration, Appl. Math. Lett. 17 (2) (2004), 133–137.

Zafar, F., Some generalizations of Ostrowski inequalities and their applications to numerical integration and special means, PhD thesis, Bahauddin Zakariya University, Multan, Pakistan, 2010.




DOI: http://dx.doi.org/10.17951/a.2021.75.2.13-29
Date of publication: 2022-02-21 20:04:35
Date of submission: 2022-02-13 21:34:18


Statistics


Total abstract view - 582
Downloads (from 2020-06-17) - PDF - 549

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2021 Martin Bohner, Asif Khan, Maria Khan, Faraz Mehmood, Muhammad Awais Shaikh