Second Note on the Definition of S₁-Convexity

Abstract

In this note, we discuss the definition of the S 1 -convexity Phenomenon. We first make use of some results we have attained for in the past, such as those contained in [1] , to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K 0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that does not properly extend K 0 in both its original and its revised version.