Young's inequality and related results on time scales

Abstract We establish the classical Young inequality on time scales as follows: a b ≤ ∫ 0 a g σ ( x ) Δ x + ∫ 0 b ( g − 1 ) σ ( y ) Δ y if g ∈ C r d ( [ 0 , c ] , R ) is strictly increasing with c > 0 and g ( 0 ) = 0 , a ∈ [ 0 , c ] , b ∈ [ 0 , g ( c ) ] . Using this inequality, we can extend Hőlder’s inequality and Minkowski’s inequality on time scales.