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First Note on the Definition of s<i>1</i>-Convexity

First Note on the Definition of s<i>1</i>-Convexity
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摘要 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. 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.
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出处 《Advances in Pure Mathematics》 2014年第12期674-679,共6页 理论数学进展(英文)
关键词 Analysis CONVEXITY DEFINITION S-Convexity GEOMETRY Analysis Convexity Definition S-Convexity Geometry
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