2010/02/12 by Douglas R. Anderson, Anderson, Douglas R., Steven Noren +3
Mathematics · #26D15 #34N05 #39A12 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #Nonlinear Differential Equations Analysis #math.CA #msc:26D15 #msc:34N05 #msc:39A12
paper · pdf · doi:10.48550/arxiv.1002.2463
8 pages
arxiv created 2010/02/12 · openalex publication_date 2010/02/12 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.