Nonlinear Functional Analysis and Applications

  • 제28권3호
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  • Pages.801-812
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  • 2023
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  • 1229-1595(pISSN)
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  • 2466-0973(eISSN)
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
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ON THE SUPERSTABILITY FOR THE p-POWER-RADICAL SINE FUNCTIONAL EQUATION

  • 투고 : 2022.12.26
  • 심사 : 2023.02.25
  • 발행 : 2023.09.15
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we investigate the superstability for the p-power-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)$$ from an approximation of the p-power-radical functional equation: $$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 and f, g, h are complex valued functions. Furthermore, the obtained results are extended to Banach algebras.

키워드

과제정보

This work was supported by Kangnam University Research Grant in 2020.

참고문헌

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