Second Note on the Definition of S1-Convexity

DOI: 10.4236/apm.2015.53015   PDF   HTML   XML   3,934 Downloads   4,391 Views   Citations

Abstract

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.

References

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[5] Dragomir, S.S. and Fitzpatrick, S. (1999) The Hadamard’s Inequality for S-Convex Functions in the Second Sense. Demonstratio Mathematica, 32, 687-696.
[6] Pinheiro, M.R. (2007) Exploring the Concept of s-Convexity. Aequationes Mathematicae, 74, 201-209.
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[9] Pinheiro, M.R. (2014) Third Note on the Shape of S-Convexity. International Journal of Pure and Applied Mathematics, 93, 729-739.

  
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