Ostrowski Inequality Theory And Application In Probability

This article mainly studies the Ostrowski and the other form of the Ostrowskiiequality theory and its application in probability theory. The most interestingdirection is the study of Ostrowski inequality form and new inequality form intime scales space. Some higher differential functions that derivatives areunbounded are obtained especially for the Ostrowski-Grüss inequality and the errorbound between Ostrowski-Like inequality and Rieman sum which approximate theintegral are analysised. Last we give new Ostrowski inequality in probability on thebasis of previous probability results.This paper consists of five parts. we briefly introduce the development ofOstrowski inequality and compare the different conclusions of Ostrowski inequalityfirstly, then we summarize most of the inequalty results.In the process of studying Ostrowski inequality, this paper presents thenecessary results about this inequality and then we analysis the connection of theseconclusions. New inequality form of higher order differential functions are obtainedby taking lower condition method. And new inequality form of Ostrowski-Grüssand Ostrowski-Like inequality and the weighting form between fixed function valueand the arithmetic mean value are given by the same method. We think thecondition that derivative is inL pspace is better than derivative is bounded. At thesame time some results about the Otrowski-Grüss inequality are obtained. The errorbound between Ostrowski-Like inequality and Rieman sum which approximates theintegral are analysised.In the fourth part, new inequalities in time sacle space are presented. On thebasis of analysising derivative inequality, some inequalities in time scale spaceespecially about derivatives inequality are given by comparing method. Finally,we improved the probability version of the Ostrowski inequality Mingjin Wanggived and obtained a new Ostrowski inequality in probability theory.