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ON A QUESTION OF J. M. RASSIAS

Part of: Real functions

Published online by Cambridge University Press:  27 September 2013

WŁODZIMIERZ FECHNER
WŁODZIMIERZ FECHNER*
Affiliation:
Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland email wlodzimierz.fechner@us.edu.pl
*
fechner@math.us.edu.pl
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Abstract

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Answering a problem posed by John Michael Rassias, we study the functional inequality

$$\begin{eqnarray*}f(x+ y+ xy)\leq f(x)+ f(y)+ f(xy),\end{eqnarray*}$$
with real unknown mapping $f$.

Keywords

functional inequalitysubadditive mappingsDini derivatives

MSC classification

Secondary: 39B62: Functional inequalities, including subadditivity, convexity, etc. 26A51: Convexity, generalizations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 3 , June 2014 , pp. 494 - 499
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Bouikhalene, B., Rassias, J. M., Charifi, A. and Kabbaj, S., ‘On the approximate solution of the Hosszú’s functional equation’, Int. J. Nonlinear Anal. Appl. 3 (1) (2012), 40–44.Google Scholar
Fechner, W., ‘A note on alienation for functional inequalities’, J. Math. Anal. Appl. 385 (1) (2012), 202–207.CrossRefGoogle Scholar
Hammer, C., ‘Über die Funktionalungleichung $f(x+ y)+ f(xy)\geq f(x)+ f(y)+ f(x)f(y)$’, Aequationes Math. 45 (2–3) (1993), 297–299.Google Scholar
Kuczma, M., An Introduction to the Theory of Functional Equations and Inequalities, Cauchy’s Equation and Jensen’s Inequality, 2nd edn. (Birkhäuser, Basel, 2009), edited and with a preface by Attila Gilányi.CrossRefGoogle Scholar
Maksa, G. and Páles, Z., ‘On Hosszú’s functional inequality’, Publ. Math. Debrecen 36 (1–4) (1989), 187–189.CrossRefGoogle Scholar
Pečarić, J. E., ‘Two remarks on Hosszú’s functional inequality’, Publ. Math. Debrecen 40 (3–4) (1992), 243–244.CrossRefGoogle Scholar
Powązka, Z., ‘Über Hosszúfunktionalungleichung und die Jensenische Integralungleichung’, Rocznik Nauk.-Dydakt. Prace Mat. 14 (1997), 121–128.Google Scholar