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Refined Stability Results of Functional Equation in Four Variables

Kim, Hark-Mahn;Lee, Soon

  • Received : 2013.03.30
  • Accepted : 2013.07.18
  • Published : 2015.03.23

Abstract

In this paper, we present the general solution of the functional equation $$rf(\frac{x+y+z+w}{s})+rf(\frac{x+y-z-w}{s})+rf(\frac{x-y+z-w}{s})+rf(\frac{x-y-z+w}{s})=tf(x)+tf(y)+tf(z)+tf(w)$$ and improve the Hyers-Ulam stability of the equation.

Keywords

quadratic functional equation;Hyers-Ulam stability

References

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Acknowledgement

Supported by : National Research Foundation (NRF)