The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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ADDITIVE ρ-FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN BANACH SPACE

  • Paokanta, Siriluk (Department of Mathematics, Research Institute for Natural Sciences, Hanyang University) ;
  • Shim, Eon Hwa (Department of Mathematics, Daejin University)
  • Received : 2018.06.08
  • Accepted : 2018.08.03
  • Published : 2018.08.31
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Abstract

In this paper, we solve the additive ${\rho}$-functional equations $$(0.1)\;f(x+y)+f(x-y)-2f(x)={\rho}\left(2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)\right)$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < 1, and $$(0.2)\;2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ${\rho}$-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.

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References

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