A symmetric Norlund sum with application to inequalities

TL;DR

This paper explores properties of a symmetric Nörlund sum and introduces quantum versions of classical inequalities like Hölder, Cauchy-Schwarz, and Minkowski, extending their applicability.

Contribution

It develops a symmetric Nörlund sum framework and derives quantum analogs of key inequalities, advancing the mathematical theory and potential applications.

Findings

Properties of the symmetric Nörlund sum are characterized.

Quantum versions of Hölder, Cauchy-Schwarz, and Minkowski inequalities are established.

The results extend classical inequalities to a quantum symmetric sum context.

Abstract

Properties of an $\alpha,\beta$-symmetric Norlund sum are studied. Inspired in the work by Agarwal et al., $\alpha,\beta$-symmetric quantum versions of Holder, Cauchy-Schwarz and Minkowski inequalities are obtained.