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On the Superstability of the p­radical Sine Type Functional Equations

김광휘
한국수학교육학회|2021.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제28권 제4호|pp. 387-398|DOI https://doi.org/10.7468/jksmeb.2021.28.4.387

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참고문헌

키워드

stabilitysuperstabilitysine functional equation
주제분류수학

초록

In this paper, we will find solutions and investigate the superstability bounded by constant for the $p$-radical functional equations as follows: \begin{equation*} f\left(\sqrt[p]{\frac{x^{p}+y^{p}}{2}}\right)^{2} -f\left(\sqrt[p]{\frac{x^{p}-y^{p}}{2}}\right)^{2}= \begin{cases} (i) \; f(x)f(g(x)g(y). \end{cases} \end{equation*} 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.

Abstract

In this paper, we will find solutions and investigate the superstability bounded by constant for the $p$-radical functional equations as follows: \begin{equation*} f\left(\sqrt[p]{\frac{x^{p}+y^{p}}{2}}\right)^{2} -f\left(\sqrt[p]{\frac{x^{p}-y^{p}}{2}}\right)^{2}= \begin{cases} (i) \; f(x)f(g(x)g(y). \end{cases} \end{equation*} 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.

참고문헌 (24)

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