On the Superstability of the p­radical Sine Type Functional Equations

Kim, Gwang Hui; Kim, Gwang Hui

doi:https://doi.org/10.7468/jksmeb.2021.28.4.387

P-ISSN3059-0604
E-ISSN3059-1309
KCI

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Vol.28 No.4

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On the Superstability of the pradical Sine Type Functional Equations

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

2021, v.28 no.4, pp.387-398

https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.4.387

Kim, Gwang Hui

Kim,, G. H. (2021). On the Superstability of the pradical Sine Type Functional Equations. , 28(4), 387-398, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.4.387

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Abstract

In this paper, we will find solutions and investigate the superstability bounded by constant for the p-radical functional equations as follows: <TEX>$f $\sqrt[p]{\frac{x^p+y^p}{2}}$ ^2-f $\sqrt[p]{\frac{x^p-y^p}{2}}$ ^2=\;\{(i)\;f(x)f(y),\\(ii)\;g(x)f(y),\\(iii)\;f(x)g(y),\\(iv)\;g(x)g(y).$</TEX> with respect to the sine functional equation, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebra.

keywords: stability, superstability, sine functional equation, cosine functional equation, p-radical functional equation

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Article Contents

Vol.28 No.4

On the Superstability of the p­radical Sine Type Functional Equations

Abstract

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

On the Superstability of the pradical Sine Type Functional Equations