<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. H. SAKER</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">RAVI. P.  AGARWAL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME NEW DYNAMIC INEQUALITIES ON DISCRETE TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A15</style></keyword><keyword><style  face="normal" font="default" size="100%">26D10</style></keyword><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">34A40. 34N05</style></keyword><keyword><style  face="normal" font="default" size="100%">39A13</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/08-dsa-113-128.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper we prove some new dynamic inequalities on discrete time scales. These new inequalities contain some generalizations of the discrete inequalities due to Hardy, Copson, Leindler and Walsh. The main results will be proved using a general algebraic inequality and Keller’s chain rule on time scales.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">213</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. H. SAKER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPLICATIONS OF OPIAL AND WIRTINGER INEQUALITIES ON ZEROS OF THIRD ORDER DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/31-DSA-31-15-new.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, for a third order differential equation, we will establish some new inequalities of Lyapunov type. These inequalities give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zeros of a solution and/or its derivatives. The main results will be proved by making use of the H¨older inequality and some generalizations of Opial and Wirtinger type inequalities. Some examples are considered to illustrate the main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">479</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">John R. Graef</style></author><author><style face="normal" font="default" size="100%">S. H. SAKER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NEW OSCILLATION CRITERIA FOR GENERALIZED SECOND-ORDER NONLINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword><keyword><style  face="normal" font="default" size="100%">34K40</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/32-DSA-30-07.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, the authors consider the second-order neutral functional differential equation&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;[ p(t) ψ( y(t) )(x′(t) )&lt;sup&gt;γ&lt;/sup&gt; ] ′ + q(t) f( y(δ(t)) ) = 0,&amp;nbsp; &amp;nbsp;t ≥ t&lt;sub&gt;0&lt;/sub&gt;,&lt;/p&gt;

&lt;p&gt;where&amp;nbsp; &amp;nbsp;x(t) = y(t) + r(t) y( τ(t) )&amp;nbsp; and&amp;nbsp; γ &amp;gt; 0&amp;nbsp; is a ratio of odd positive integers. They establish some new sufficient conditions for oscillation of all solutions that are substantial improvements to some existing results in the literature. Some examples are included to illustrate the main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">455</style></section></record></records></xml>