An Extension of a Ger’s Result

Marinescu, Dan Ştefan; Monea, Mihai

doi:10.1515/amsil-2017-0008

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.

References

[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.
Search in Google Scholar Back to article
[2] Bourbacuµ N., Problem 11641, Amer. Math. Monthly 119 (2012), no. 4, 345.
Search in Google Scholar Back to article
[3] Breckner W.W., Trif T., Convex Functions and Related Functional Equations, Selected Topics, Cluj University Press, Cluj, 2008.
Search in Google Scholar Back to article
[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), 200-217.10.1016/0041-5553(67)90040-7
Open DOI Search in Google Scholar Back to article
[5] Daróczy Z., Páles Z., Convexity with given weight sequence, Stochastica 11 (1987), no. 1, 5-12.
Search in Google Scholar Back to article
[6] Dragomir S.S., Pearce C.E.M., Pecaric J., Means, g-convex dominated functions & Hadamard-type inequalities, Tamsui Oxf. J. Math. Sci. (1561-8307) 18 (2002), no. 2, 161-173.
Search in Google Scholar Back to article
[7] Ger R., A functional inequality, Amer. Math. Monthly 121 (2014), no. 2, 174-175.
Search in Google Scholar Back to article
[8] Ger R., On a problem, 15th International Conference on Functional Equations and Inequalities, May 19-25, 2013.
Search in Google Scholar Back to article
[9] Hartman P., On functions representable as a difference of two convex functions, Pacific J. Math. 9 (1957), 707-713.
Search in Google Scholar Back to article
[10] Niculescu C.P., Persson L.-E., Convex Functions and Their Applications: A Contemporary Approach, Springer, New York, 2006.10.1007/0-387-31077-0_2
Search in Google Scholar Back to article
[11] Páles Z., Nonconvex functions and separation by power means, Math. Inequal. Appl. 3 (2000), no. 2, 169-176.
Search in Google Scholar Back to article
[12] Olbrys A., A support theorem for delta (s; t)-convex mappings, Aequationes Math. 89 (2015), 937-948.10.1007/s00010-014-0290-6
Search in Google Scholar Back to article
[13] Veselý L.L., Zajícek L., Delta-convex mappings between Banach spaces and applications, Dissertationes Math. 289, Polish Acad. Sci. Inst. Math., Warsaw, 1989.
Search in Google Scholar Back to article

An Extension of a Ger’s Result

Abstract

Paradigm

My account