New version of generalized Ostrowski-Gruss type inequality
DOI:
https://doi.org/10.24193/subbmath.2021.3.03Keywords:
Ostrowski-Gru¨ss type inequality, Korkine’s identity, probability density function.Abstract
Ostrowski inequality is one of the celebrated inequalities in Mathematics. The main purpose of our study is to generalize the result of Ostrowski-Gru¨ss type inequality for first differentiable mappings and apply it to probability density functions, composite quadrature rules and special means.
Mathematics Subject Classification (2010): 26D15, 26D20, 26D99.
References
Anastassiou, G.A., Multivariate Ostrowski type inequalities, Acta Math. Hungar., 76(1997), 267-278.
Barnett, N.S., Dragomir, S.S., Sofo, A., Better bounds for an inequality of Ostrowski type with applications, Demonstratio Math., 34(2001), no. 3, 533-542. Preprint RGMIA Res. Rep. Coll., 3(2000), no. 1, Article 11.
Cebysev, P.L., Sur les expressions approximatives des integrales definies par les autres prises entre les memes limites, Proc. Math. Soc. Charkov, 2(1882), 93-98.
Cerone, P., Dragomir, S.S., Roumeliotis, J., A new generalization of Ostrowski integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means, Appl. Math. Lett., 13(2000), no. 1, 19-25.
Cheng, X.L., Improvement of some Ostrowski-Gruss type inequalities, Comput. Math. Appl., 42(2001), no. 1/2, 109-114.
Dragomir, S.S., Sofo, A., An integral inequality for twice differentiable mappings and applications, Tamkang J. Math., 31(2000), no. 4, 257-266. Preprint RGMIA Res. Rep. Coll., 2(1999), no. 2.
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(1997), no. 11, 16-20.
Ghazi, W., Qayyum, A., A note on new Ostrowski type inequalities using a generalized kernel, Bulletin of Mathematical Analysis and Application, 9(2017), 74-91.
Gruss, G., Uber das Maximum des absoluten Betrages von, Math. Z., 39(1935), no. 1, 215-226.
Irshad, N., Khan, A.R., Shaikh, M.A., Generalized Ostrowski type inequality with applications in numerical integration, probability theory and special means, In Dr. Manuel Alberto M. Ferreira (Eds.), Current Topics in Mathematics and Computer Science, Vol. 9 (74-91). B P International, India-United Kingdom, 2021.
Matic, M., Pecaric, J.E., Ujevic, N., Improvement and further generalization of some inequalities of Ostrowski-Gruss type, Comput. Math. Appl., 39(2000), no. 3/4, 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. No. 544-576, (1976), 155-158.
Mitrinovic, D.S., Pecaric, J.E., Fink, A.M., Inequalities for Functions and their Integrals and Derivatives, Kluwer Academic Publishers, 1991.
Mitrinovic, D.S., Pecaric, J.E., Fink, A.M., Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1991.
Ostrowski, A., Uber die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert, Comment. Math. Helv., 10(1938), 226-227.
Ujevic, N., New bounds for the first inequality of Ostrowski-Gruss type and applications, Computers and Mathematics with Applications, 46(2003), 421-427.
Zafar, F., Mir, N.A., A generalization of Ostrowski-Gruss type inequality for first differentiable mappings, Tamsui Oxford J. Math. Sci., 26(2010), no. 1, 61-76.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
