Opial inequalities on time scales

Dynamic Systems and Applications 24 (2015) 229-242 IMPROVEMENTS OF DYNAMIC OPIAL-TYPE INEQUALITIES AND APPLICATIONS

ABSTRACT. In this paper, we present some new improvements of dynamic Opial-type inequalities of first and higher order on time scales. We employ the new inequalities to prove several results related to the spacing between consecutive zeros of a solution and/or a zero of its derivative of a second-order dynamic equation with a damping term. The main results are proved by making use of a recently...

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.

Dynamic Opial diamond-α integral inequalities involving the power of a function

In this paper, we present some new dynamic Opial-type diamond alpha inequalities on time scales. The obtained results are related to the function [Formula: see text].

Time Scales Inequalities

Here first we collect and develop necessary background on time scales required for this article. Then we present time scales integral inequalities of types: Poincaré, Sobolev, Opial, Ostrowski and Hilbert–Pachpatte. We give also the generalized analogs of all these inequalities involving high order delta derivatives of functions on time scales. We finish with lots of applications: all these ine...

Generalized diamond-a dynamic opial inequalities

* Correspondence: billur@cankaya. edu.tr Department of Mathematics and Computer Science, Çankaya University, Ankara, Turkey Full list of author information is available at the end of the article Abstract We establish some new dynamic Opial-type diamond alpha inequalities in time scales. Our results in special cases yield some of the recent results on Opial’s inequality and also provide new esti...

Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales