Converses of Nabla Pachpatte-Type Dynamic Inequalities on Arbitrary Time Scales

Abstract

Reverse Pachpatte-type inequalities are concave generalizations of the well-known Bennett-Leindler-type inequalities. We establish reverse nabla Pachpatte-type dynamic inequalities taking account of concavity. It is the first time that converses of Pachpatte-type inequalities are obtained in the nabla time scale calculus as well as for its special cases such as continuous and discrete cases and for the dual results obtained in the delta time scale calculus. Moreover, some of our results extend the related ones when concavity has been removed.