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Stability of Mixed Additive–Quadratic and Additive–Drygas Functional Equations

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Abstract

In this paper, using the Baire category theorem we investigate the Hyers–Ulam stability problem of mixed additive–quadratic and additive–Drygas functional equations

$$\begin{aligned} 2f(x+y) + f(x-y) - 3f(x) -3f(y)&= 0,\\ 2f(x+y) + f(x-y) - 3f(x) -2f(y) -f(-y)&= 0 \end{aligned}$$

on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.

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Acknowledgements

First of all, I would like to express my gratitude to Professor Jaeyoung Chung (1961–2016), who coached the stability of functional equations in restricted domains. Secondly, I want to thank Yumin Ju, who contributed to Lemma 1.2 [6, Lemma 2.1] and derived a result related to it when he was a student at Kunsan National University. Finally, I would like to thank Professor John Michael Rassias for helping me to study the stability of mixed functional equations.

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Authors and Affiliations

  1. Department of Mathematics and Hwangrong Talent Education Institute, Kunsan National University, Gunsan, 54150, Republic of Korea

    Chang-Kwon Choi

  2. Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju, 54896, Republic of Korea

    Bogeun Lee

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  1. Chang-Kwon Choi
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Choi, CK., Lee, B. Stability of Mixed Additive–Quadratic and Additive–Drygas Functional Equations. Results Math 75, 38 (2020). https://doi.org/10.1007/s00025-020-1163-z

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