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In this paper, we solve and investigate the superstability of the $p$-radical functional equations \begin{align*} f\left(\sqrt[p]{x^{p}+y^{p}}\right) &-f\left(\sqrt[p]{x^{p}-y^{p}}\right)=\lambda f(x) g(y),\\ f\left(\sqrt[p]{x^{p}+y^{p}}\right) &-f\left(\sqrt[p]{x^{p}-y^{p}}\right)=\lambda g(x) f(y), \end{align*} 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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참고문헌 (22)
참고문헌 신청
J. d'Alembert / 1769 / Memoire sur les Principes de Mecanique / Hist. Acad. Sci. Paris :278~286
M. Almahalebi / 2021 / Superstability of p-radical functional equations related to Wilson-Kannappan-Kim functional equations / Results Math 76:97
T. Aoki / 1950 / On the stability of the linear transformation in Banach spaces / J. Math. Soc. Japan 2:64~66
R. Badora / 1998 / On the stability of cosine functional equation / Rocznik Naukowo-Dydak. Prace Mat 15:1~14
R. Badora, R. Ger / 2002 / On some trigonometric functional inequalities, in Functional Equations-Results and Advances :3~15
M. Almahalebi / 2021 / Superstability of p-radical functional equations related to Wilson-Kannappan-Kim functional equations / Results Math 76:97
T. Aoki / 1950 / On the stability of the linear transformation in Banach spaces / J. Math. Soc. Japan 2:64~66
R. Badora / 1998 / On the stability of cosine functional equation / Rocznik Naukowo-Dydak. Prace Mat 15:1~14
R. Badora, R. Ger / 2002 / On some trigonometric functional inequalities, in Functional Equations-Results and Advances :3~15
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