Korean J. Math. Vol. 29 No. 4 (2021) pp.765-774
DOI: https://doi.org/10.11568/kjm.2021.29.4.765

Superstability of the p-radical trigonometric functional equation

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Published: Dec 30, 2021
Keywords:
superstability, p-radical equation, cosine functional equation, sine functional equation, Wilson equation, Kim equation.
Mathematics Subject Classification:
39B82, 39B52

Main Article Content

Gwang Hui Kim
Department of Mathematics, Kangnam University, Yongin 16979, Republic of Korea.

Abstract

In this paper, we solve and investigate the superstability of the p-radical functional equations

f(xp+ypp)−f(xp−ypp)=λf(x)g(y),f(xp+ypp)−f(xp−ypp)=λg(x)f(y),

which is related to the trigonometric(Kim's type) functional equations, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebras.



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