On a conjectured inequality in convex analysis in the case of the unit ball of lp^n, 1<= p<= infinity

TL;DR

This paper provides an alternative proof of a conjecture related to convex analysis for the unit p-ball in R^n, using classical analysis tools and properties of the gamma function.

Contribution

It offers a new proof of Kuperberg's conjecture for the unit p-ball, avoiding complex functions like polygamma functions used in previous proofs.

Findings

Confirmed the conjecture for the unit p-ball in R^n

Provided a proof using basic gamma function properties

Simplified the proof approach with classical analysis tools

Abstract

We re-confirm, for the case of the unit p-ball of R^n, one of recent conjectures of G.Kuperberg on centrally symmetric convex bodies.This conjecture was very recently confirmrd for this particular case by D.A.Gutierrez using polygamma functions and convexity theory.We present another proof using only the basic properties of gamma function and mildly advanced classical analysis tools.