Diamond-Alpha Hardy-Copson Type Dynamic Inequalities-I

Abstract

The dual results, the 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 Hardy-Copson type dynamic inequalities are established by developing a new 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 the similar theorems in the delta and nabla approaches but do not exist in the diamond-alpha calculus. © 2025 selection and editorial matter, Ravi P. Agarwal, Bipan Hazarika and Sanket Tikare. All rights reserved.