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ON THE STABILITY OF A CAUCHY-JENSEN FUNCTIONAL EQUATION

Jun, Kil-Woung;Lee, Yang-Hi;Cho, Young-Sun

  • Published : 2008.07.31

Abstract

In this paper, we prove the stability of a Cauchy-Jensen functional equation $$2f(x+y,\;\frac{z+w}2)$$=f(x, z)+f(x, w)+f(y, z)+f(y, w) in the sense of Th. M. Rassias.

Keywords

stability;Cauchy-Jensen mapping;functional equation

References

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  4. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300 https://doi.org/10.2307/2042795
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Cited by

  1. On an equation characterizing multi-cauchy-jensen mappings and its Hyers-Ulam stability vol.35, pp.6, 2015, https://doi.org/10.1016/S0252-9602(15)30059-X
  2. On Stability and Hyperstability of an Equation Characterizing Multi-Cauchy–Jensen Mappings vol.73, pp.2, 2018, https://doi.org/10.1007/s00025-018-0815-8