# 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)
• Accepted : 2013.03.11
• Published : 2013.03.25
• 79 6

#### 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.

#### Acknowledgement

Supported by : Gongju National University of Education

#### References

1. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
2. S.M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.
3. 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
4. D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222-224.
5. 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