On the characterization of Jensen m-convex polynomials

Abstract

The main objective of this research is to characterize all the real polynomial functions of degree less than the fourth which are Jensen m-convex on the set of non-negative real numbers. In the first section, it is established for that class of functions what conditions must satisfy a particular polynomial in order to be starshaped on the same set. Finally, both kinds of results are combined in order to find examples of either Jensen m-convex functions which are not starshaped or viceversa.

Keywords

• real polynomial function
• starshaped function
• m-convex function
• jensen mconvex function
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