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.

Highlights

  • NotationWe use the symbols from [1] here:. s2 for the variable s , 0 < s2 ≤ 1 , used for the second type of s -convexity

  • If we make the domain of the convex functions be inside of the set of the non-negative real numbers, we have the class

  • We prove that PROBLEM 1, PROBLEM 2, and PROBLEM 3 will make the proof not be a mathematical proof

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Summary

Notation

We use the symbols from [1] here:. s2 for the variable s , 0 < s2 ≤ 1 , used for the second type of s -convexity. We use the symbols from [1] here:. S2 for the variable s , 0 < s2 ≤ 1 , used for the second type of s -convexity. Remark 1 The class 1-convex functions is a subclass of the class convex functions. If we make the domain of the convex functions be inside of the set of the non-negative real numbers, we have the class. How to cite this paper: Pinheiro, I.M.R. (2014) First Note on the Definition of s1-Convexity. 1-convex functions: K11 ≡ K12 ≡ K0

Definition
Theorems That We Discuss Here
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