Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SEVERAL STABILITY PROBLEMS OF A QUADRATIC FUNCTIONAL EQUATION

  • Cho, In-Goo (FACULTY OF LIBERAL EDUCATION UNIVERSITY OF INCHEON) ;
  • Koh, Hee-Jeong (DEPARTMENT OF MATHEMATICS EDUCATION DANKOOK UNIVERSITY)
  • Received : 2010.01.18
  • Published : 2011.01.31
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Abstract

In this paper, we investigate the stability using shadowing property in Abelian metric group and the generalized Hyers-Ulam-Rassias stability in Banach spaces of a quadratic functional equation, $f(x_1+x_2+x_3+x_4)+f(-x_1+x_2-x_3+x_4)+f(-x_1+x_2+x_3)+f(-x_2+x_3+x_4)+f(-x_3+x_4+x_1)+f(-x_4+x_1+x_2)=5{\sum\limits_{i=1}^4}f(x_i)$. Also, we study the stability using the alternative fixed point theory of the functional equation in Banach spaces.

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References

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