On Extending the Domain of (Co)convex Polynomials: Update

Abstract

In this study, we will employ a distinct methodology compared to the prevailing techniques in the literature. The literature,
mostly concentrate on the partitioning of convex sets using hyperplanes. The focus of our inquiry is the behaviour of a convex set that
encompasses the domain of convex and coconvex polynomials, which we will refer to as (co)convex polynomials. The primary aim of
this study is to investigate the following enquiries: Given that D is the domain of (co)convex polynomials of ∆
(2)
(Ys) for s ≥ 0 and
x ∈ D, the question is whether x qualifies as an inflection point within D