A support theorem for delta (s, t)-convex mappings

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• 作者：Andrzej Olbry?
• 关键词：39B62 ; 26A51 ; 26B25 ; Convexity ; Jensen convexity ; (s ; t) ; convexity ; delta ; convexity
• 刊名：Aequationes Mathematicae
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：89
• 期：3
• 页码：937-948
• 全文大小：446 KB
• 参考文献：1.Daróczy Z., Páles Zs.: Convexity with given infinite weight sequences. Stochastica 11, 5-2 (1987)MATH MathSciNet
  2.Ger R.: Stability aspects of delta-convexity. In: Rassias, Th.M., Tabor, J. (eds.) Stability of Hyers–Ulam type, pp. 99-09. Hardonic Press, Palm Harbor (1994)
  3.Ger R.: Stability of polynomial mappings controlled by n-convex functionals. In: Agorwal, R.P. (ed.) Inequalities and applications, a volume dedicated to W.Walter, World Scientific Series in Applied Analysis, pp. 255-68. World Scientific Publishing Company, Singapore (1994)
  4.Kominek, Z.: Convex Functions in Linear Spaces. Prace Naukowe Uniwersytetu ?la?skiego w Katowicach nr 1087, Katowice (1989)
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  8.Kuhn N.: On the structure of (s, t)-convex functions. General Inequalities 5. Internat. Ser. Numer. Math. 80, 161-74 (1987)
  9.Kuczma M.: An Introduction to the Theory of Functional Equations and Inequalities. Birkh?user, Basel, Boston, Berlin (2009)View Article MATH
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  12.Rodé, G.: Eine abstrakte Version des Satzes von Hahn–Banach. Arch. Math. 31 (1978)
  13.Vesely, L., Zajic?ek, L.: Delta-convex mappings between Banach spaces and applications. Dissertationes Math., Polish Scientific Publishers (289), Warszawa (1989)
  
• 作者单位：Andrzej Olbry? (1)
  
  1. Institute of Mathematics, Silesian University, Bankowa 14, 40-007, Katowice, 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

In the present paper a notion of delta (s, t)-convexity in the sense of Vesely and Zajic?ek is studied as a natural generalization of the classical (s, t)-convexity. The main result of this paper is a support theorem for delta (s, t)-convex mappings.