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GENERALIZED HYERES{ULAM STABILITY OF A QUADRATIC FUNCTIONAL EQUATION WITH INVOLUTION IN QUASI-${\beta}$-NORMED SPACES

  • Janfada, Mohammad (Department of Mathematics, Sabzevar Tarbiat Moallem University) ;
  • Sadeghi, Ghadir (Department of Mathematics, Sabzevar Tarbiat Moallem University)
  • Received : 2010.06.24
  • Accepted : 2010.10.26
  • Published : 2011.09.30

Abstract

In this paper, using a fixed point approach, the generalized Hyeres-Ulam stability of the following quadratic functional equation $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=3(f(x)+f(y)+f(z))$ will be studied, where f is a function from abelian group G into a quasi-${\beta}$-normed space and ${\sigma}$ is an involution on the group G. Next, we consider its pexiderized equation of the form $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=g(x)+g(y)+g(z)$ and its generalized Hyeres-Ulam stability.

Keywords

References

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