Approximate convexity with the standard deviation’s error

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• 作者：Marek ?o?dak
• 关键词：26A51 ; 26B25 ; Approximate convexity
• 刊名：Aequationes Mathematicae
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：89
• 期：3
• 页码：449-457
• 全文大小：452 KB
• 参考文献：1.Boros Z.: An inequality for the Takagi functions. Math. Inequalities Appl. 11/4, 757-65 (2008)View Article MathSciNet
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  7.Rudin W.: Principles of Mathematical Analysis. Mc Graw-Hill, New York (1964)MATH
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  9.Tabor Ja., Tabor Jó., ?o?dak M.: Approximately convex functions on topological vector spaces. Publ. Math. Debr. 77/1-, 115-23 (2010)
  
• 作者单位：Marek ?o?dak (1)
  
  1. Faculty of Mathematics and Natural Science, University of Rzeszów, Prof. St. Pigonia 1, 35-310, Rzeszow, Poland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Combinatorics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8903

文摘

Functions \({f\colon D\rightarrow \mathbb{R}}\) defined on an open convex subset of \({\mathbb{R}^n}\) satisfying the approximate type convexity condition with bound of the form \({\varepsilon \sqrt{t(1-t)} \|x-y\|}\) are considered. We discuss properties concerning such functions characteristic for convex functions.