论文标题
Ostrowski类型不等式和一些选定的正交公式
Ostrowski type inequalities and some selected quadrature formulae
论文作者
论文摘要
在本次调查文件中研究了一些选择的Ostrowski类型不平等以及与数值集成的联系，该调查文件致力于对D.S. Mitrinovic教授的记忆，他在25年前离开了我们。本文的第一部分简要介绍了他对不平等理论发展的重要影响。 Beside some basic facts on quadrature formulas and an approach for estimating the error term using Ostrowski type inequalities and Peano kernel techniques, we give several examples of selected quadrature formulas and the corresponding inequalities, including the basic Ostrowski's inequality (1938), inequality of Milovanovic and Pecaric (1976) and its modifications, inequality of Dragomir, Cerone and Roumeliotis（2000），猜测和Schmeisser（2002）的对称不平等和Franjic（2009）的不平等不平等，以及Alomari（2012）的四点对称不等式以及由Liu和Park（2017年给出的双重内部节点）的变体。
Some selected Ostrowski type inequalities and a connection with numerical integration are studied in this survey paper, which is dedicated to the memory of Professor D.S. Mitrinovic, who left us 25 years ago. His significant influence to the development of the theory of inequalities is briefly given in the first section of this paper. Beside some basic facts on quadrature formulas and an approach for estimating the error term using Ostrowski type inequalities and Peano kernel techniques, we give several examples of selected quadrature formulas and the corresponding inequalities, including the basic Ostrowski's inequality (1938), inequality of Milovanovic and Pecaric (1976) and its modifications, inequality of Dragomir, Cerone and Roumeliotis (2000), symmetric inequality of Guessab and Schmeisser (2002) and asymmetric inequality of Franjic (2009), as well as four point symmetric inequalites by Alomari (2012) and a variant with double internal nodes given by Liu and Park (2017).
