Some new estimates of the ‘Jensen gap’

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• 作者：Shoshana Abramovich ; Lars-Erik Persson
• 关键词：26D10 ; 26D15 ; 26B25 ; Jensen’s inequality ; convex function ; γ ; superconvex functions ; superquadratic functions ; Taylor expansion
• 刊名：Journal of Inequalities and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,333 KB
• 参考文献：1. Jensen, JLWV: Om konvexe Funktioner og Uligeder mellem Middelvaerdier. Nyt Tidsskr. Math. 16B, 49-69 (1905) (in Danish)
  2. Jensen, JLWV: Sur les fonctions convexes et les inegalités entre les moyennes. Acta Math. 30, 175-193 (1906) (in French) CrossRef MathSciNet
  3. Persson, L-E, Samko, N: Inequalities and Convexity, Operator Theory: Advances and Applications, vol. 242, 29 pp. Birkhäuser, Basel (2014)
  4. Abramovich, S, Jameson, G, Sinnamon, G: Refining of Jensen’s inequality. Bull. Math. Soc. Sci. Math. Roum. 47, 3-14 (2004) MathSciNet
  5. Abramovich, S, Persson, L-E: Some new scales of refined Hardy type inequalities via functions related to superquadracity. Math. Inequal. Appl. 16, 679-695 (2013) MathSciNet
  6. Abramovich, S, Persson, L-E, Samko, N: On γ-quasiconvexity, superquadracity and two sided reversed Jensen type inequalities. Math. Inequal. Appl. 18(2), 615-627 (2015) MathSciNet
  7. Oguntuase, J, Persson, L-E: Refinement of Hardy’s inequalities via superquadratic and subquadratic functions. J. Math. Anal. Appl. 339, 1305-14012 (2008) CrossRef MathSciNet
  8. Abramovich, S, Persson, L-E: Some new refined Hardy type inequalities with breaking points \(p=2\) and \(p=3\) . In: Proceedings of the IWOTA 2011, vol. 236, pp. 1-10. Birkhäuser, Basel (2014)
  9. Abramovich, S, Persson, L-E, Samko, N: Some new scales of refined Jensen and Hardy type inequalities. Math. Inequal. Appl. 17, 1105-1114 (2014) MathSciNet
  10. Walker, SG: On a lower bound for Jensen inequality. SIAM J. Math. Anal. (to appear)
  11. Dragomir, SS: Jensen integral inequality for power series with nonnegative coefficients and applications. RGMIA Res. Rep. Collect. 17, 42 (2014)
  
• 作者单位：Shoshana Abramovich (1)
  Lars-Erik Persson (2) (3)
  
  1. Department of Mathematics, University of Haifa, Haifa, Israel
  2. Department of Engineering Sciences and Mathematics, Luleå University of Thechnology, Luleå, 971 87, Sweden
  3. UiT The Arctic University of Norway, P.O. Box 385, Narvik, 8505, Norway
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

Let \(( \mu,\Omega ) \) be a probability measure space. We consider the so-called ‘Jensen gap’ $$ J ( \varphi,\mu,f ) = \int_{\Omega}\varphi \bigl( f ( s ) \bigr)\,d\mu ( s ) -\varphi \biggl( \int_{\Omega }f ( s )\,d\mu ( s ) \biggr) $$