Newton-type inequalities associated with convex functions via quantum calculus

Abstract

In this paper, we firstly establish an identity by using the notions of quantum derivatives and integrals. Using this quantum identity, quantum Newton-type inequalities associated with convex functions are proved. We also show that the newly established inequalities can be recaptured into some existing inequalities by taking <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>q</mml:mi> <mml:mo class="MathClass-rel" stretchy="false">→</mml:mo> <mml:msup><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo class="MathClass-bin" stretchy="false">−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>. Finally, we give mathematical examples of convex functions to verify the newly established inequalities.

Locations

• Miskolc mathematical notes/Mathematical notes - View - PDF
• Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) - View - PDF