<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The main objective of this research is to characterize all the real polynomial functions of degree less than the fourth which are Jensen <italic>m</italic>-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 <italic>m</italic>-convex functions which are not starshaped or viceversa.</p></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.

On the characterization of Jensen <italic>m</italic>-convex polynomials

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On the characterization of Jensen -convex polynomials

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...

On the characterization of Jensen m-convex polynomials

Published Online: Jul 28, 2018

Page range: 140 - 148

Received: Sep 15, 2017

Accepted: May 10, 2018

DOI: https://doi.org/10.1515/mjpaa-2017-0012

Keywords
Real polynomial function, starshaped function, -convex function, Jensen convex function

© 2018 Teodoro Lara et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On the characterization of Jensen m-convex polynomials

Published Online: Jul 28, 2018

Page range: 140 - 148

Received: Sep 15, 2017

Accepted: May 10, 2018

DOI: https://doi.org/10.1515/mjpaa-2017-0012

KeywordsReal polynomial function, starshaped function, -convex function, Jensen convex function

© 2018 Teodoro Lara et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Real polynomial function, starshaped function, -convex function, Jensen convex function