Duality principle of time scales and inequalities

Abstract

Here we adopt, develop further and use the principle of duality in time scales Caputo, [Time scales: from nabla calculus to delta calculus and vice versa via duality, arxiv: 0910.0085v1 [math.OC] 1 Oct. 2009]. Using this principle and based on a variety of important delta inequalities we produce the corresponding nabla ones. We give several applications.

Keywords:

• times scales
• nabla and delta calculus
• duality principle
• Ostrowski inequality
• Poincare inequality
• Sobolev inequality
• Opial inequality
• Hilbert–Pachpatte inequality

AMS Subject Classifications::

• 26D15
• 26E70
• 39A12
• 93C70