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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.28 No.4

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On the Superstability of the p­radical Sine Type Functional Equations

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2021, v.28 no.4, pp.387-398
https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.4.387
Kim, Gwang Hui
Kim,, G. H. (2021). On the Superstability of the p­radical Sine Type Functional Equations. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 28(4), 387-398, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.4.387

Abstract

In this paper, we will find solutions and investigate the superstability bounded by constant for the p-radical functional equations as follows: <TEX>$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=\;\{(i)\;f(x)f(y),\\(ii)\;g(x)f(y),\\(iii)\;f(x)g(y),\\(iv)\;g(x)g(y).$</TEX> 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.

keywords
stability, superstability, sine functional equation, cosine functional equation, p-radical functional equation

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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