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.
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.
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Douglas R. Anderson Concordia College, Department of Mathematics and Computer Science Moorhead, MN 56562, USA email: andersod@cord.edu http://www.cord.edu/faculty/andersod/ |
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Steven Noren Concordia College Moorhead, MN 56562, USA email: srnoren@cord.edu |
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Brent Perreault Concordia College Moorhead, MN 56562, USA email: bmperrea@cord.edu |
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