 
Summary: Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 74, pp. 110.
ISSN: 10726691. 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 piecewisemonotone functions as well.
1. introduction
In 1912, Young [14] presented the following highly intuitive integral inequality,
namely that any realvalued continuous function f : [0, ) [0, ) satisfying
f(0) = 0 with f strictly increasing on [0, ) satisfies
ab
a
0
f(t)dt +
