Multiplicative Ostrowski and Trapezoid Inequalities

Pietro Cerone (), Sever S. Dragomir () and Eder Kikianty ()
Additional contact information
Pietro Cerone: La Trobe University
Sever S. Dragomir: Victoria University
Eder Kikianty: University of Johannesburg

A chapter in Handbook of Functional Equations, 2014, pp 57-73 from Springer

Abstract: Abstract We introduce the multiplicative Ostrowski and trapezoid inequalities, that is, providing bounds for the comparison of a function f and its integral mean in the following sense: $$\begin{aligned} f(x) {\rm exp}\! \left[\!-\frac{1}{b-a}\int_a^b\!\! \log f(t)\, dt\!\right]\! \text{and}\!\ f(b)^{\frac{b-x}{b-a}} f(a)^{\frac{x-a}{b-a}} {\rm exp}\! \left[\!-\frac{1}{b-a}\int_a^b\!\! \log f(t)\, dt\!\right].\end{aligned}$$ We consider the cases of absolutely continuous and logarithmic convex functions. We apply these inequalities to provide approximations for the integral of f; and the first moment of f around zero, that is, $\int_{a}^{b}xf(x)dx$ ; for an absolutely continuous function f on [ $a,b$ ].

Keywords: Ostrowski inequality; Trapezoid inequality; Logarithmic convex function (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1246-9_4

Ordering information: This item can be ordered from
http://www.springer.com/9781493912469

DOI: 10.1007/978-1-4939-1246-9_4

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().