The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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HYERS-ULAM STABILITY OF AN ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN BANACH SPACES

  • Park, Choonkil (Research Institute for Natural Sciences, Hanyang University) ;
  • Yun, Sungsik (Department of Financial Mathematics, Hanshin University)
  • Received : 2018.01.04
  • Accepted : 2018.05.04
  • Published : 2018.05.31
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Abstract

In this paper, we introduce and solve the following additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) $${\parallel}f(x+y+z)-f(x)-f(y)-f(z){\parallel}{\leq}{\parallel}{\rho}_1(f(x+z)-f(x)-f(z)){\parallel}+{\parallel}{\rho}_2(f(y+z)-f(y)-f(z)){\parallel}$$, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero complex numbers with ${\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}$ < 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) in complex Banach spaces.

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References

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