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STABILITY OF AN EXPONENTIAL-MONOMIAL FUNCTIONAL EQUATION

Published online by Cambridge University Press:  28 March 2018

CHANG-KWON CHOI Open the ORCID record for CHANG-KWON CHOI [Opens in a new window]
CHANG-KWON CHOI*
Affiliation:
Department of Mathematics and Liberal Education Institute, Kunsan National University, Gunsan 54150, Republic of Korea email [email protected]
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Abstract

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Let $N$ be a fixed positive integer and $f:\mathbb{R}\rightarrow \mathbb{C}$. As a generalisation of the superstability of the exponential functional equation we consider the functional inequalities

$$\begin{eqnarray}\displaystyle & \displaystyle \big|f\big(\!\sqrt[N]{x^{N}+y^{N}}\big)-f(x)f(y)\big|\leq \unicode[STIX]{x1D719}(x), & \displaystyle \nonumber\\ \displaystyle & \displaystyle \big|f\big(\!\sqrt[N]{x^{N}+y^{N}}\big)-f(x)f(y)\big|\leq \unicode[STIX]{x1D713}(x,y) & \displaystyle \nonumber\end{eqnarray}$$
for all $x,y\in \mathbb{R}$, where $\unicode[STIX]{x1D719}:\mathbb{R}\rightarrow \mathbb{R}^{+}$ is an arbitrary function and $\unicode[STIX]{x1D713}:\mathbb{R}^{2}\rightarrow \mathbb{R}^{+}$ satisfies a certain condition.

Keywords

exponential functional equationexponential-monomial functional equationstability

MSC classification

Primary: 39B82: Stability, separation, extension, and related topics
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 3 , June 2018 , pp. 471 - 479
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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