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ON A QUESTION OF J. M. RASSIAS

Published online by Cambridge University Press:  27 September 2013

WŁODZIMIERZ FECHNER*
Affiliation:
Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland email [email protected]
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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 $f$.

Type
Research Article
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), 4044.Google Scholar
Fechner, W., ‘A note on alienation for functional inequalities’, J. Math. Anal. Appl. 385 (1) (2012), 202207.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), 297299.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), 187189.CrossRefGoogle Scholar
Pečarić, J. E., ‘Two remarks on Hosszú’s functional inequality’, Publ. Math. Debrecen 40 (3–4) (1992), 243244.CrossRefGoogle Scholar
Powązka, Z., ‘Über Hosszúfunktionalungleichung und die Jensenische Integralungleichung’, Rocznik Nauk.-Dydakt. Prace Mat. 14 (1997), 121128.Google Scholar