Generalizations of Sherman’s inequality by Lidstone’s interpolating polynomial

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• 作者：Ravi P Agarwal ; Slavica Ivelić Bradanović…
• 关键词：26D15 ; majorization ; n ; convexity ; Schur ; convexity ; Sherman’s theorem ; Lidstone interpolating polynomial ; Čebyšev functional ; Grüss type inequalities ; Ostrowsky type inequalities ; exponentially convex functions ; log ; convex functions ; means
• 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：1,629 KB
• 参考文献：1. Hardy, GH, Littlewood, JE, Pólya, G: Inequalities, 2nd edn. Cambridge University Press, Cambridge (1952) MATH
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• 作者单位：Ravi P Agarwal (1)
  Slavica Ivelić Bradanović (2)
  Josip Pečarić (3)
  
  1. Department of Mathematics, Texas A&M, University-Kingsville, Rhode Hall 217B, MSC 172, Kingsville, TX, 78363-8202, USA
  2. Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Matice hrvatske 15, Split, 21000, Croatia
  3. Faculty of Textile Technology, University of Zagreb, Prilaz Baruna Filipovića 30, Zagreb, 10000, Croatia
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

In majorization theory, the well-known majorization theorem plays a very important role. A more general result was obtained by Sherman. In this paper, concerning 2n-convex functions, we get generalizations of these results applying Lidstone’s interpolating polynomials and the Čebyšev functional. Using the obtained results, we generate a new family of exponentially convex functions. The results are some new classes of two-parameter Cauchy type means. Keywords majorization n-convexity Schur-convexity Sherman’s theorem Lidstone interpolating polynomial Čebyšev functional Grüss type inequalities Ostrowsky type inequalities exponentially convex functions log-convex functions means