Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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AN ADDITIVE FUNCTIONAL INEQUALITY

  • Received : 2014.04.06
  • Accepted : 2014.06.09
  • Published : 2014.06.30
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Abstract

In this paper, we solve the additive functional inequality $${\parallel}f(x)+f(y)+f(z){\parallel}{\leq}{\parallel}{\rho}f(s(x+y+z)){\parallel}$$, where s is a nonzero real number and ${\rho}$ is a real number with ${\mid}{\rho}{\mid}$ < 3. Moreover, we prove the Hyers-Ulam stability of the above additive functional inequality in Banach spaces.

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References

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