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Volume 10, Issue 3, Article 76 |
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Iteration Semigroups with Generalized Convex, Concave and Affine Elements
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Authors: |
Dorota Krassowska, |
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Keywords:
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Iteration semigroup, Convex (concave, affine)-functions with respect to some functions. |
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Date Received:
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31/07/2008 |
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Date Accepted:
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22/03/2009 |
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Subject Codes: |
Primary 39B12, 26A18; Secondary 54H15.
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Editors: |
Attila Gilányi, |
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Abstract: |
Given continuous functions  and  of two variables, it is shown that if in a continuous iteration semigroup with only  -convex or -concave elements there are two -affine elements, then  and every element of the semigroup is -affine. Moreover, all functions in the semigroup either are -convex or -concave.
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