A note on Ostrowski's inequality

Abstract

This paper deals with the problem of estimating the deviation of the values of a function from its mean value. We consider the following special cases: (i) the case of random variables (attached to arbitrary probability fields); (ii) the comparison is performed additively or multiplicatively; (iii) the mean value is attached to a multiplicative averaging process.

A New Generalized Inequality for Covariance in N Dimensions

“…Until nowadays, the works of Chebyshev, Ostrowski, and Grüss have continued to inspire active mathematical research focused on inequalities/estimates of (co)variance. This fact is clearly documented by rich literature dealing with the subject [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. For the purposes of the present article we specifically highlight an inequality for covariance which was derived recently by He and Wang in [20].…”

Types of Statistical Indicators Characterized by 2-Pre-Hilbert Spaces

“…Florea and Niculescu in Reference [20] treated the problem of estimating the deviation of the values of a function from its mean value. The estimation of the deviation of a function from its mean value is characterized below.…”

“…Next, we can write some equalities and inequalities, using several results from Section 2, related to variance, covariance and the standard deviation of vectors x, y ∈ X. Therefore, from relations (8), (10), (11), (15), (18)- (20), (22), (25), we obtain the following relations: where a, b ∈ R. By dividing by u = 0, we deduce the relation a x u + be = w u , where e = u u , so e = 1. Therefore, we obtain a = ( w u , x u |e)…”