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A Fixed Point Approach to the Stability of Quadratic Equations in Quasi Normed Spaces

Mirmostafaee, Alireza Kamel

  • Received : 2008.10.12
  • Accepted : 2008.12.11
  • Published : 2009.12.31

Abstract

We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

Keywords

quasi p-norm;quadratic functional equation;fixed point alternative;Hyers-Ulam-Rassias stability

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