OSTROWSKI TYPE INEQUALITIES AND SOME SELECTED QUADRATURE FORMULAE

Applicable Analysis and Discrete Mathematics

article

Gradimir V. Milovanović¹ 

[1] Serbian Academy of Sciences and Arts;University of Niˇs, Faculty of Sciences and Mathematics

关键词: Inequalities of Ostrowski type;    Norm;    Quadrature rules;    Peano kernel;    Best constant;   

DOI  :  10.2298/AADM200609054M

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

Some selected Ostrowski type inequalities and a connection with numericalintegration are studied in this survey paper, which is dedicated to the memoryof Professor D. S. Mitrinovi´c, who left us 25 years ago. His significant influence to the development of the theory of inequalities is briefly given in thefirst section of this paper. Beside some basic facts on quadrature formulas andan approach for estimating the error term using Ostrowski type inequalitiesand Peano kernel techniques, we give several examples of selected quadratureformulas and the corresponding inequalities, including the basic Ostrowski’sinequality (1938), inequality of Milovanovi´c and Peˇcari´c (1976) and its modifications, inequality of Dragomir, Cerone and Roumeliotis (2000), symmetricinequality of Guessab and Schmeisser (2002) and asymmetric inequality ofFranji´c (2009), as well as four point symmetric inequalites by Alomari (2012)and a variant with double internal nodes given by Liu and Park (2017).

【 授权许可】

Unknown