충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제35권4호
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  • Pages.315-327
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  • 2022
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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TRANSFERRED SUPERSTABILITY OF THE p-RADICAL SINE FUNCTIONAL EQUATION

  • Kim, Gwang Hui (Department of Mathematics Kangnam University) ;
  • Roh, Jaiok (Ilsong Liberal Art Schools(Mathematics) Hallym University)
  • 투고 : 2022.11.02
  • 심사 : 2022.11.21
  • 발행 : 2022.11.30
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초록

In this paper, we investigate the transferred superstability for the p-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from the p-radical functional equations: $$f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)g(y),\;\\f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)h(y),$$ where p is an odd positive integer, λ is a positive real number, and f is a complex valued function. Furthermore, the results are extended to Banach algebras. Therefore, the obtained result will be forced to the pre-results(p=1) for this type's equations, and will serve as a sample to apply it to the extension of the other known equations.

키워드

과제정보

This paper was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1A2C109489611).

참고문헌

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