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

Abstract

We use the xed alternative theorem to establish Hyers{Ulam{Rassias stabil- ity 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 approx- imately 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 map- ping. We also give a few applications of our results in some special cases.