Generalized diamond alpha bennett-leindler-type dynamic inequalities

Abstract

The dual results; delta and nabla inequalities and their special cases; continuous and discrete inequalities are unified into diamond alpha case and new forms of such results as well as new diamond alpha Bennett-Leindler-type dynamic inequalities are established by developing a novel method, which does not require the Integration by Parts Formula and the Fundamental Theorem of Calculus. These theorems are standard arguments in the proofs of Bennett-Leindler-type dynamic inequalities in the delta and nabla approaches but do not follow naturally in the diamond alpha calculus.