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.
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).
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