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
YOUNG'S INTEGRAL INEQUALITY WITH UPPER AND
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.
In 1912, Young  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