Second Note on the Definition of S1-Convexity

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Second Note on the Definition of S₁-Convexity ()

I. M. R. Pinheiro^*

RGMIA, AMS, PROz., Melbourne, Australia.

DOI: 10.4236/apm.2015.53015 PDF HTML XML 3,940 Downloads 4,401 Views Citations

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.

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Pinheiro, I. (2015) Second Note on the Definition of S₁-Convexity. Advances in Pure Mathematics, 5, 127-130. doi: 10.4236/apm.2015.53015.

Conflicts of Interest

The authors declare no conflicts of interest.

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