An extension of a Ger’s result



Abstract

The aim of this paper is to extend a result presented by Roman Ger during the 15th International Conference on Functional Equations and Inequalities. First, we present some necessary and sufficient conditions for a continuous function to be convex. We will use these to extend Ger’s result. Finally, we make some connections with other mathematical notions, as g-convex dominated function or Bregman distance.


Keywords

convex functions; continuous functions; differentiable functions

1. Baillon J.B., Haddad G., Quelques propriétés des opérateurs angle-bornés et n-cycliquement monotones, Israel J. Math. 26 (1977), no. 2, 137–150.
2. Bourbăcuţ N., Problem 11641, Amer. Math. Monthly 119 (2012), no. 4, 345.
3. Breckner W.W., Trif T., Convex Functions and Related Functional Equations, Selected Topics, Cluj University Press, Cluj, 2008.
4. Bregman L., The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming, USSR Comput. Math. Math. Phys. 7 (1967), 200–217.
5. Daróczy Z., Páles Z., Convexity with given weight sequence, Stochastica 11 (1987), no. 1, 5–12.
6. Dragomir S.S., Pearce C.E.M., Pečarić J., Means, g-convex dominated functions & Hadamard-type inequalities, Tamsui Oxf. J. Math. Sci. (1561–8307) 18 (2002), no. 2, 161–173.
7. Ger R., A functional inequality, Amer. Math. Monthly 121 (2014), no. 2, 174–175.
8. Ger R., On a problem, 15th International Conference on Functional Equations and Inequalities, May 19–25, 2013.
9. Hartman P., On functions representable as a difference of two convex functions, Pacific J. Math. 9 (1957), 707–713.
10. Niculescu C.P., Persson L.-E., Convex Functions and Their Applications: A Contemporary Approach, Springer, New York, 2006.
11. Páles Z., Nonconvex functions and separation by power means, Math. Inequal. Appl. 3 (2000), no. 2, 169–176.
12. Olbryś A., A support theorem for delta (s, t)-convex mappings, Aequationes Math. 89 (2015), 937–948.
13. Veselý L.L., Zajíček L., Delta-convex mappings between Banach spaces and applications, Dissertationes Math. 289, Polish Acad. Sci. Inst. Math., Warsaw, 1989.
Download

Published : 2017-08-05


MarinescuD. Ştefan, & MoneaM. (2017). An extension of a Ger’s result. Annales Mathematicae Silesianae, 32, 263-274. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13925

Dan Ştefan Marinescu 
National College Iancu de Hunedoara, Romania  Romania
Mihai Monea  mihaimonea@yahoo.com
National College Decebal & University Politehnica Bucharest, Romania  Romania



The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.

  1. License
    This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license.
  2. Author’s Warranties
    The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.
  3. User Rights
    Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.
  4. Co-Authorship
    If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.