%0 Journal Article %T Second Note on the Definition of S<sub>1</sub>-Convexity %A I. M. R. Pinheiro %J Advances in Pure Mathematics %P 127-130 %@ 2160-0384 %D 2015 %I Scientific Research Publishing %R 10.4236/apm.2015.53015 %X In this note, we discuss the definition of the S₁-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 K₀ 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 K₀ in both its original and its revised version. %K Analysis %K Convexity %K Definition %K s-Convexity %K Geometry %K Shape %K S-Convexity %K s-Convex Function %K S-Convex Function %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=54592