Some Generalizations of Opial’s Inequalities on Time Scales

Some Opial‐Type Inequalities on Time Scales

“…Let Ì be a time scale with a, b ∈ Ì and p, q positive real numbers such that pq > 0 and p q > 1, and let r, s be nonnegative rd-continuous functions on a, b Ì such that .30 , we obtain the following special case from Theorem 2.4, which improves the inequality 1.21 obtained by Wong et al23 . Let Ì be a time scale with a, b ∈ Ì and p, q positive real numbers such that p q > 1, and let r be a nonnegative rd-continuous function on a, X Ì such that Δt < ∞.…”

Dynamic Inequalities On Time Scales

“…The results in this section are adapted from [49,91,127,136,139,149]. To prove the results we need the following theorem [111, p. 338].…”

Opial and Pólya Type Inequalities Via Convexity

“…The proof of the following inequality follows immediately from the inequality (19) by applying Jensen's inequality.…”

“…Wong et al [19] and Srivastava et al [17] proved that if s(t) is a positive and non-increasing function on [a, b] T , then…”