First Note on the Definition of s1-Convexity

I. M. R. Pinheiro^1*

¹P.O. Box 12396 A’Beckett St, Melbourne, Victoria, Australia, 8006.

DOI: 10.4236/apm.2014.412076                

Abstract

In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.

Keywords

Analysis, Convexity, Definition, S-Convexity, Geometry

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Pinheiro, M.R. (2008) Convexity Secrets. Trafford, Canada, ISBN 1-4251-3821-7.
[2]	Pearce, C.E.M. and Dragomir, S.S. (2000) Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs. http://rgmia.org/papers/monographs/Master.pdf
[3]	Hudzik, H. and Maligranda, L. (1994) Some Remarks on s-Convex Functions. Aequationes Mathematicae, 48, 100-111. http://dx.doi.org/10.1007/BF01837981
[4]	Pinheiro, M.R. (2013) Minima Domain Intervals and the S-Convexity, as Well as the Convexity, Phenomenon. Advances in Pure Mathematics, 3, 457-458.
[5]	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).