التفاصيل البيبلوغرافية
| العنوان: |
Superstability of the $ p $-power-radical functional equation related to sine function equation. |
| المؤلفون: |
Hwang, Hye Jeang, Kim, Gwang Hui |
| المصدر: |
Electronic Research Archive; 2023, Vol. 31 Issue 10, p1-16, 16p |
| مصطلحات موضوعية: |
FUNCTIONAL equations, SINE function, STABILITY theory, INTEGERS, BANACH algebras |
| مستخلص: |
In this paper, we find solutions and investigate the superstability bounded by a function (Gǎvruta sense) for the p -power-radical functional equation related to sine function equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = f (x) f (y) from an approximation of the p -power-radical functional equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = g (x) h (y) , where p is a positive odd integer, and f , g and h are complex valued functions on R . Furthermore, the obtained results are extended to Banach algebras. In this paper, we find solutions and investigate the superstability bounded by a function (Gǎvruta sense) for the p -power-radical functional equation related to sine function equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = f (x) f (y) from an approximation of the p -power-radical functional equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = g (x) h (y) , where p is a positive odd integer, and f , g and h are complex valued functions on R . Furthermore, the obtained results are extended to Banach algebras. [ABSTRACT FROM AUTHOR] |
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