Generalized Ostrowski inequalities and computational integration
Keywords:Ostrowski Inequality, Quadrature Rules
We state and prove three generalized results related to Ostrowski inequality by using differentiable functions which are bounded, bounded below only and bounded above only, respectively. From our proposed results we get number of established results as our special cases.
Some applications in numerical integration are also given which gives us some standard and nonstandard quadrature rules.
W. G. Alshanti and G. V. Milovanovic, Double-sided inequalities of Ostrowski’s Type and some Applications, J. Computational Analysis and Applications, 28, (2020), pp. 724–736.
E. F. Beckenbach and R. Bellman, Springer-Verlag, Berlin-Gottinggon-Heidelberg,1961, https://doi.org/10.1007/978-3-642-64971-4
S. S. Dragomir, P. Cerone and J. Roumeliotis, A new generalization of Ostrowski integral inequality for mappings whose derivatives are bounded and applications in nuumerical integration and for special means, Appl. Math. lett. 13 No. 1, (2000), pp. 19–25, https://doi.org/10.1007/978-3-642-64971-4
W. Gautschi, Numerical Analysis: An Introduction, Birkahauser, Boston 1997
G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge University Press, 1934.
M. Imtiaz, N. Irshad, and A. R. Khan, Generalization of weighted Ostrowski integral inequality for twice differentiable mappings, Adv. Inequal. Appl., 2016 (2016), pp. 1–17, Article No. 20.
N. Irshad, A. R. Khan and A. Nazir, Extension of Ostrowki type inequality via moment generating function, Adv. Inequal. Appl.,2020(2) (2020), pp. 1–15, https://doi.org/10.28919/aia/3600
N. Irshad, A. R. Khan, And M. A. Shaikh, Generalized Weighted Ostrowski-Gruss Type Inequality with Applications, Global J. Pure Appl. Math., 15 (5) (2019), pp. 675–692, https://doi.org/10.28919/aia/3998
N. Irshad, A. R. Khan, M. A. Shaikh, Generalization of Weighted Ostrowski Inequality with Applications in Numerical Integration, Adv. Ineq. Appl., 2019 (7) (2019),pp. 1–14.
N. Irshad and A. R. Khan, On Weighted Ostrowski Gruss Inequality with Applications, TJMM, 10(1) (2018), pp. 15–22
N. Irshad and A. R. Khan, Some Applications of Quadrature Rules for Mappings on Lp[u, v] Space via Ostrowski-type Inequality, J. Num. Anal. Approx. Theory,46(2)(2017), pp. 141-149.
N. Irshad and A. R. Khan, , J. Math. Anal.,8(1)(2017), pp. 79–102.
M. Masjed-Jamei and S. S. Dragomir, Generalization of Ostrowski Gruss Inequality,World Scientific12(2) (2014), pp. 117–130, https://doi.org/10.1142/s0219530513500309
M. Masjed-Jamei and S. S. Dragomir, An analogue of the Ostrowski Inequality and applications, Filomat 28(2) (2014), pp. 373–381, https://doi.org/10.2298/fil1402373m
G. V. Milovanovi c, On some Integral Inequalities, Univ. Beograd. Publ. Elektrotehn.Fak. Ser. Mat. Fiz., pp. 498–541 (1975), pp. 97–106.
G. V. Milovanovic and J. E. Pecaric, On Generalization of the Inequality of A.Ostrowski and Some related Applications, Univ. Beograd. Publ. Elektrotehn. Fak. Ser.Mat. Fiz., pp. 544–576 (1976), pp. 155–158.
D. S. Mitrinovi c , J. E. Pecaric , and A. M. Fink, “Classical and New Inequalities in Analysis” Kluwer Academic Publishers, Dordrecht (1991).
D. S. Mitrinovic , J. E. Pecaric, and A. M. Fink, “Inequalities Involving Functions and their Integrals and Derivatives”. Kluwer Academic Publishers, Dordrecht (1991).
A. M. Ostrowski, Uber die absolutabweichung einer differentiebaren funktion von ihrenintegralmittelwert, Comment. Math. Helv.,10(1938), pp. 226–227, https://doi.org/10.1007/bf01214290
M. A. Shaikh, A. R. Khan and N. Irshad, Generalized Ostrowski Inequality with Applications in Numerical Integration and Special Means, Adv. Inequal Appl., 2018 (2018):7, pp. 1–22, https://doi.org/10.28919/aia/3553
N. Ujevic, A generalization of Ostrowski’s inequality and applications in numerical integration, Appl. Math. Lett.,17, (2004), pp. 133–137, https://doi.org/
M. J. Vivas-Cortez, A. Kashuri, R. Liko and J. E. Hernandez Hernandez, Quantum estimates of Ostrowski inequalities for generalized φ-convex functions, Symmetry,11(12)(2019), pp. 1–16, https://doi.org/10.3390/sym11121513
M. J. Vivas-Cortez, A. Kashuri, R. Liko and J. E. Hernandez Hernandez, Some inequalities using generalized convex functions in quantum analysis, Symmetry, 11(11)(2019), pp. 1-14, https://doi.org/10.3390/sym11111402