First Note on the Definition of s*1*-Convexity

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.

Cite this paper

Pinheiro, I. (2014) First Note on the Definition of s*1*-Convexity. *Advances in Pure Mathematics*, **4**, 674-679. doi: 10.4236/apm.2014.412076.

Pinheiro, I. (2014) First Note on the Definition of s

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).

[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).