We establish the classical Young inequality on time scales as follows: ab ≤ ∫ a 0 g (x) x + ∫ b 0 (g−1)σ (y) y if g ∈ Crd ([0, c],R) is strictly increasing with c > 0 and g(0) = 0, a ∈ [0, c], b ∈… (More)

The purpose of this work is to establish the timescale version of Lyapunov’s inequality as follows: Let x(t) be a nontrivial solution of (r(t)x (t)) + p(t)x (t) = 0 on [a, b] satisfying x(a) = x(b) =… (More)

Under some suitable assumptions, we show that the n + 2 order non-linear boundary value problems (BVP1) (E1) [φp(u (n)(t))]′′ = f (t, u(t), u(1)(t), . . . , u(n+1)(t)) (BC1)… (More)

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 fi (t) t ) ≥ ( 2n ∫ 1 0 tn t )( n ∏ i=1 ∫ 1 0 fi (t) t ) if fi (i =… (More)