Properties and characterizations of convex functions on time scales
Abstract
In this research we deal with algebraic properties and characterizations of convex functions in the context of a time scale; this notion of convexity has been studied for some other authors but the setting of properties are establish here. Moreover, characterizations, a separation theorem and an inequality of Jensen type for this class of functions are shown as well.
Keywords
time scales; convex functions; Jensen inequality
References
2. Dinu C., Convex functions on time scales, An. Univ. Craiova Ser. Mat. Inform. 35 (2008), 87–96.
3. Dinu C., Hermite-Hadamard inequality on time scales, J. Inequal. Appl. 2008 (2008), Art. ID 287947, 24 pp.
4. Hilger S., Analysis on measure chains–a unified approach to continuous and discrete calculus, Results Math. 18 (1990), 18–56.
5. Kaymakçalan B., A survey of dynamic systems on measure chains, Funct. Differ. Equ. 6 (1999), 125–135.
6. Merentes N., Rivas S., The development of the concept of convex function, XXVI Escuela Venezolana de Matemáticas, Venezuela, 2013 (in Spanish).
7. Mozyrska D., Torres D.F.M., The natural logarithm on time scales, J. Dyn. Syst. Geom. Theor. 7 (2009), 41–48.
8. Olbryś A., On separation by h-convex functions, Tatra Mt. Math. Publ. 62 (2015), 105–111.
9. Roberts A.W., Varberg D.E., Convex functions, Academic Press, New York, 1973.
Departamento de Física y Matemáticas, Universidad de Los Andes, Venezuela Venezuela, Bolivarian Republic of
Escuela de matemáticas, Universidad Central de Venezuela Venezuela, Bolivarian Republic of
Departamento de Física y Matemáticas, Universidad de Los Andes, Venezuela Venezuela, Bolivarian Republic of
Departamento de Física y Matemáticas, Universidad de Los Andes, Venezuela Venezuela, Bolivarian Republic of
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