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The renowned Jensen inequality is established on time scales as follows: f b a |h(s)|g(s)∆s b a |h(s)|∆s ≤ b a |h(s)|f (g(s))∆s b a |h(s)|∆s , if f , g and h satisfy some suitable conditions.
We establish the classical Young inequality on time scales as follows: ab ≤ a 0 g σ (x))x + b 0 (g −1) σ (y))y if g ∈ C rd ([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 H˝ older's inequality and Minkowski's inequality on time scales.
Using Kransnoskii's fixed point theorem, the authors obtain the existence of multiple solutions of the following boundary value problem () 1 2 BVP E u t f t u t u t t p n n
We establish Anderson's inequality on time scales as follows: 1 0 n i=1 f σ i (t) t ≥ 1 0 (t + σ (t)) n t n i=1 1 0 f i (t))t ≥ 2 n 1 0 t n t n i=1 1 0 f i (t))t if f i (i = 1,. .. , n) satisfy some suitable conditions.