Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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STABILITY OF A QUADRATIC-ADDITIVE TYPE FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN NORMED SPACES

  • Lee, Chang-Ju (Department of Mathematics Education, Gongju National University of Education) ;
  • Lee, Yang-Hi (Department of Mathematics Education, Gongju National University of Education)
  • Received : 2013.02.07
  • Accepted : 2013.03.11
  • Published : 2013.03.25
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Abstract

In this paper, we investigate the stability for the functional equation $$2f(x+y)+f(x-y)+f(y-x)-f(2x)-f(2y)=0$$ in non-Archimedean normed spaces.

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References

  1. T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64-66. https://doi.org/10.2969/jmsj/00210064
  2. D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222-224.
  3. M.S. Moslehian and Th. M. Rassias, Stability of functional equations in non-Archimedean spaces, Appl. Anal. Discrete Math. 1 (2007), 325-334. https://doi.org/10.2298/AADM0702325M
  4. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
  5. S.M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.