JIPAM

Iteration Semigroups with Generalized Convex, Concave and Affine Elements  
 
  Authors: Dorota Krassowska,  
  Keywords: Iteration semigroup, Convex (concave, affine)-functions with respect to some functions.  
  Date Received: 31/07/2008  
  Date Accepted: 22/03/2009  
  Subject Codes:

Primary 39B12, 26A18; Secondary 54H15.

  
  Editors: Attila Gilányi,  
 
  Abstract:

Given continuous functions $ M$ and $ N$ of two variables, it is shown that if in a continuous iteration semigroup with only $ (M,N)$-convex or $ (M,N)$-concave elements there are two $ (M,N)$-affine elements, then $ M=N$ and every element of the semigroup is $ M$-affine. Moreover, all functions in the semigroup either are $ M$-convex or $ M$-concave. ;


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