Generalized Hardy, Copson, Leindler and Bennett inequalities on time scales. Issue 5 (8th October 2013)

• Record Type: Journal Article
• Authors: Saker, S. H.; O'Regan, D.; Agarwal, R.
• Is Part Of: Mathematische Nachrichten. Volume 287:Issue 5/6(2014)
• Page Start: 686
• Page End: 698
• Publication Date: 2013-10-08
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201300010
• Languages: English
• ISSNs: 0025-584X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>In this paper, we prove some new dynamic inequalities on time scales using Hölder's inequality and Keller's chain rule on time scales. These inequalities, as special cases when the time scale <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg537sdg3r" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:dummy:mana201300010:equation:mana201300010-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="double-struck">T</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:math></alternatives> and when <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg537sdg26" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:dummy:mana201300010:equation:mana201300010-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="double-struck">T</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="double-struck">N</mml:mi></mml:mrow></mml:math></alternatives>, contain some generalizations of integral and discrete inequalities due to Hardy, Copson, Leindler and Bennett.</p> </abstract>