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
References
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.
National College Iancu de Hunedoara, Romania Romania
National College Decebal & University Politehnica Bucharest, Romania Romania
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