APM  Vol.5 No.3 , March 2015
Second Note on the Definition of S1-Convexity
Author(s) I. M. R. Pinheiro*
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.

Cite this paper
Pinheiro, I. (2015) Second Note on the Definition of S1-Convexity. Advances in Pure Mathematics, 5, 127-130. doi: 10.4236/apm.2015.53015.
References
[1]   Pinheiro, M.R. (2013) Minima Domain Intervals and the S-Convexity, as Well as the Convexity, Phenomenon. Advances in Pure Mathematics, 3, 457-458.

[2]   Pinheiro, M.R. (2014) First Note on the Definition of s1-Convexity. Advances in Pure Mathematics, 4, 674-679.

[3]   Hudzik, H. and Maligranda, L. (1994) Some Remarks on s-Convex Functions. Aequationes Mathematicae, 48, 100-111.

[4]   Dragomir, S.S. and Pearce, C.E.M. (2002) Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA, Monographs. Online at rgmia.vu.edu.au.

[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.

[7]   Pinheiro, M.R. (2004) Exploring the Concept of s-Convexity. Proceedings of the 6th WSEAS Int. Conf. on Mathematics and Computers in Physics (MCP '04).

[8]   Pinheiro, M.R. (2008) Convexity Secrets. Trafford Canada.

[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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