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Companion Inequalities to Jensen's Inequality for $m$-convex and $(\alpha,m)$-convex Functions  
 
  Authors: M. Klaricic Bakula, Josip E. Pecaric, M. Ribičić,  
  Keywords: $m$-convex functions, $ (alpha,m) $-convex functions, Jensen's inequality, Slater's inequality, Hermite-Hadamard's inequalities, Giaccardi's inequality, Fejér's inequalities.  
  Date Received: 21/04/06  
  Date Accepted: 06/12/06  
  Subject Codes:

26A51, 26B25.

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

General companion inequalities related to Jensen's inequality for the classes of $ m$-convex and $ left( alpha,mright) $-convex functions are presented. We show how Jensen's inequality for these two classes, as well as Slater's inequality, can be obtained from these general companion inequalities as special cases. We also present several variants of the converse Jensen's inequality, weighted Hermite-Hadamard's inequalities and inequalities of Giaccardi and Petrovic for these two classes of functions.;


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