Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 74, pp. 110. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
 

Summary: Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 74, pp. 110.
ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
ftp ejde.math.txstate.edu
YOUNG'S INTEGRAL INEQUALITY WITH UPPER AND
LOWER BOUNDS
DOUGLAS R. ANDERSON, STEVEN NOREN, BRENT PERREAULT
Abstract. Young's integral inequality is reformulated with upper and lower
bounds for the remainder. The new inequalities improve Young's integral
inequality on all time scales, such that the case where equality holds becomes
particularly transparent in this new presentation. The corresponding results
for difference equations are given, and several examples are included. We
extend these results to piecewise-monotone functions as well.
1. introduction
In 1912, Young [14] presented the following highly intuitive integral inequality,
namely that any real-valued continuous function f : [0, ) [0, ) satisfying
f(0) = 0 with f strictly increasing on [0, ) satisfies
ab
a
0
f(t)dt +

  

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

 

Collections: Mathematics