Some new Opial dynamic inequalities with weighted functions on time scales

Some New Opial Dynamic Inequalities with Weighted Functions on Time Scales

In this paper we prove some new dynamic inequalities with two weight functions and some new dynamic inequalities with two unknown functions of Opial type on time scales. The main results will be proved by employing Hölder’s inequality, the chain rule and some basic algebraic inequalities. Mathematics subject classification (2010): 26A15, 26D10, 26D15, 39A13, 34A40.

Some Opial-Type Inequalities on Time Scales

and Applied Analysis 3 where r t is positive and continuous function with ∫X a dt/r t < ∞, and if x b 0, then ∫b X |x t |∣∣x′ t ∣∣dt ≤ 1 2 ∫b

Opial inequalities on time scales

We present a version of Opial’s inequality for time scales and point out some of its applications to so-called dynamic equations. Such dynamic equations contain both differential equations and difference equations as special cases. Various extensions of our inequality are offered as well.

Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales

Some Hardy Type Inequalities with Weighted Functions via Opial Type Inequalities

In this paper, we will prove several new inequalities of Hardy type with explicit constants. The main results will be proved using generalizations of Opial's inequality.