Quasi-Jensen functions
Abstract
There is defined quasi-Jensen function as a solution of a certain functional inequality which generalizes the classical Jensen equation: f((x+y)/2) = (f(x)+f(y))/2. The introduced inequality is analogous to the inequality which defines J. Tabor's quasi-additive functions. The main result of this paper is to show strong relationship between quasi-Jensen and quasi-additive functions.
References
1. M. Kuczma, An introduction to the theory of functional equations and inequalities. Cauchy's equation and Jensen's inequality, Polish Scientific Publishers (PWN), Silesian University, Warszawa-Kraków-Katowice, 1985.
2. J. Tabor, On functions behaving like additive functions, Aequationes Math. 35 (1988), 164-185.
3. J. Tabor, Quasi-additive functions, Aequationes Math. 39 (1990), 179-197.
2. J. Tabor, On functions behaving like additive functions, Aequationes Math. 35 (1988), 164-185.
3. J. Tabor, Quasi-additive functions, Aequationes Math. 39 (1990), 179-197.
ChmielińskiJ. (1992). Quasi-Jensen functions. Annales Mathematicae Silesianae, 6, 30-41. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/14265
Jacek Chmieliński
Instytut Matematyki, Wyższa Szkoła Pedagogiczna im. Komisji Edukacji Narodowej w Krakowie Poland
Instytut Matematyki, Wyższa Szkoła Pedagogiczna im. Komisji Edukacji Narodowej w Krakowie Poland
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