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The aim of this paper is to obtain the general solution of the 2-variable radical functional equations $$f\left(\sqrt[k]{x^{k}+z^{k}} ,\sqrt[\ell]{y^{\ell}+w^{\ell}}\right)=f(x,y)+f(z,w),\;\;\;x,y,z,w\in \mathbb{R}, $$for $f$ a mapping from the set of all real numbers $\mathbb{R}$ into a vector space, where $k$ and $\ell$ are fixed positive integers. Also using the fixed point result of Brzd\k{e}k and Ciepli\'{n}ski \cite[Theorem 1]{krs} in $(2,\beta)$-Banach spaces, we prove the generalized hyperstability results of the 2-variable radical functional equations. In the end of this paper we derive some consequences from our main results.
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참고문헌 (47)
참고문헌 신청
M.R. Abdollahpour / 2016 / Hyers–Ulam stability of associated Laguerre differential equations in a subclass of analytic functions / Journal of Mathematical Analysis and Applications 437(1):605~612
M. R. Abdollahpour / 2019 / Hyers-Ulam stability of hypergeometric differential equations / Aequationes Math 93(4):691~698
J. Acz´el / 1989 / Functional equations in several variables / Cambridge University Press
T. Aoki / 1950 / On the stability of the linear transformation in Banach spaces / J. Math. Soc. Japan 2:64~66
D. G. Bourgin / 1951 / Classes of transformations and bordering transformations / Bull. Amer. Math. Soc 57:223~237
M. R. Abdollahpour / 2019 / Hyers-Ulam stability of hypergeometric differential equations / Aequationes Math 93(4):691~698
J. Acz´el / 1989 / Functional equations in several variables / Cambridge University Press
T. Aoki / 1950 / On the stability of the linear transformation in Banach spaces / J. Math. Soc. Japan 2:64~66
D. G. Bourgin / 1951 / Classes of transformations and bordering transformations / Bull. Amer. Math. Soc 57:223~237
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