Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 74, pp. 1-10.

Title: Young's integral inequality with upper and lower bounds
       
Authors: Douglas R. Anderson (Concordia College, Moorhead, MN, USA)
         Steven Noren    (Concordia College, Moorhead, MN, USA)
	 Brent Perreault (Concordia College, Moorhead, MN, USA)

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.

Submitted February 14, 2011. Published June 15, 2011.
Math Subject Classifications: 26D15, 39A12, 34N05.
Key Words: Young's inequality; monotone functions;
           Pochhammer lower factorial; difference equations; 
	   time scales.