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Stability of D’Alembert’s Functional Equation with Perturbations of All Variables

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Abstract

Let \({G}\) be a commutative group and \({f : G\to \mathbb{C}}\). In this paper, we consider the mixed stability of d’Alembert’s functional equation

$$\left|f(x+y)+f(x-y)-2f(x)f(y)\right|\leq \phi(x, y)$$

for all \({x, y\in G}\), where \({\phi : G \times G \to \mathbb{R}^{+}}\) satisfies a certain condition.

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  1. Department of Mathematics, Kunsan National University, Kunsan, 573-701, Republic of Korea

    Jaeyoung Chung

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  1. Jaeyoung Chung
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Correspondence to Jaeyoung Chung.

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Chung, J. Stability of D’Alembert’s Functional Equation with Perturbations of All Variables. Results Math 71, 1015–1021 (2017). https://doi.org/10.1007/s00025-015-0526-3

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  • DOI: https://doi.org/10.1007/s00025-015-0526-3

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