On a functional equation that has the quadratic-multiplicative property

Abstract

In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation:ϕ(st−uv)+ϕ(sv+tu)=[ϕ(s)+ϕ(u)][ϕ(t)+ϕ(v)]\phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v)]by using the direct method and the fixed point method.

Keywords

• fixed point method
• hyers-ulam stability
• quadratic functional equation
• direct method
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