Inequalities for Stieltjes integrals with convex integrators and applications
type: Item
instance of: scholarly article
title: Inequalities for Stieltjes integrals with convex integrators and applications
zbMATH Open document ID: 1116.26004
published in: Applied Mathematics Letters
publication date: 2007-02-19T00:00:00Z
review text: The author considers the following functional: \[ D(f:u):= \int^b_a f(x)du(x)-(u(b)-u(a)) {1\over b-a} \int^b_a f(t)\,dt \] provided that the Stieltjes integral and Riemann integral exist. The main aim of this work is to establish sharp inequalities for the functional \(D(.,.)\) on the assumption that the integrator \(u\) in the Stieltjes integral \(\int^b_a f(x) du(x)\) is convex on \([a,b]\). Applications for the Chebyshev functional of two Lebesgue integrable functions are also given.
Mathematics Subject Classification ID: 26A42
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 5128099
zbMATH Keywords: Grüss inequality
zbMATH Keywords: Chebyshev inequality
zbMATH Keywords: convex functions
author: Silvestru Sever Dragomir
reviewed by: Octavian Lipovan
MaRDI profile type: Publication
full work available at URL: j.aml.2006.02.027
OpenAlex ID: W2011083840
cites work: Q4922454
cites work: A Grüss type inequality for mappings of bounded variation and applications to numerical analysis
cites work: Q4242904
DOI: 10.1016/J.AML.2006.02.027
description: scientific article; zbMATH DE number 5128099