Weighted Ostrowski-Grüss type inequalities

Authors

  • Ana Maria ACU Lucian Blaga University of Sibiu, Department of Mathematics and Informatics Str. Dr. I. Ratiu, No.5-7, RO-550012 Sibiu, Romania e-mail: acuana77@yahoo.com https://orcid.org/0000-0003-1192-2281
  • Heiner GONSKA University of Duisburg-Essen, Faculty of Mathematics Forsthausweg 2, 47057 Duisburg, Germany e-mail: heiner.gonska@uni-due.de

Keywords:

Ostrowki-Grüss type inequalities, modulus of smoothness, least concave majorant of modulus of continuity.

Abstract

Several inequalities of Ostrowski-Grüss-type available in the literature are generalized considering the weighted case of them. Involving the least concave majorant of the modulus of continuity we provide upper bounds of our inequalities.

Mathematics Subject Classification (2010): 26D15, 26A15, 39B62.

References

Anastassiou, G.A., Ostrowski type inequalities, Proc. Amer. Math. Soc., 123(1995), 3775-3781.

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

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, Computers Math. Appl., 33(1997), 16-20.

Gavrea, B., Gavrea, I., Ostrowski type inequalities from a linear functional point of view, J. Inequal. Pure Appl. Math., 1(2000), article 11.

Gonska, H., Rasa, I., Rusu, M.D., Generalized Ostrowski-Gruss-type inequalities, Results. Math. 62(2012), 311-318.

Matic, M., Pecaric, J., Ujevic, N., Improvement and further generalization of some inequalities of Ostrowski Gruss type, Computers Math. Applic., 39(2000) no. 3/4, 161-175.

Milovanovic, G.V, On some integral inequalities, Univ. Beograd. Publ. Elektotehn. Fak, Ser. Mat. Fiz. no. 498-541 (1975), 119-124.

Milovanovic, G.V, Pecaric, J.E, On generalization of the inequality of A. Ostrowski and some related applications, Univ. Beograd. Publ. Elektotehn. Fak, Ser. Mat. Fiz. no. 544-576 (1976), 155-158.

Roumeliotis, J., Product inequalities and applications in numerical integration, Ostrowski type inequalities and applications in numerical integration (S.S. Dragomir and Th. M. Rassias, Eds.), Kluwer Academic, 2001, 373-416.

Roumeliotis, J., Improved weighted Ostrowski-Gruss type inequalities, Inequality Theory and Applications, Nova Sci Publ, Hauppauge, NY, 3(2003), 153-160.

Semenov, E.M., Mitjagin, B.S., Lack of interpolation of linear operators in spaces of smooth functions, Math. USSR-Izv., 11(1977), 1229-1266.

STUDIA UBB MATHEMATICA, Volume 60 (LX), No. 2, June 2015

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Published

2015-06-30

How to Cite

ACU, A. M., & GONSKA, H. (2015). Weighted Ostrowski-Grüss type inequalities. Studia Universitatis Babeș-Bolyai Mathematica, 60(2), 183–192. Retrieved from https://studia.reviste.ubbcluj.ro/index.php/subbmathematica/article/view/5716

Issue

Volume 60, No. 2, June 2015

Section

Articles

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