A fixed point approach to the stability of the functional equation related to distance measures
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Abstract
In this paper, by using fixed point theorem, we obtain the stability of the following functional equations
\begin{align*}
f(pr,qs)+g(ps,qr)&=\theta(p,q, r,s)f(p,q)h(r,s) \\
f(pr,qs)+g(ps,qr)&=\theta(p,q, r,s)g(p,q)h(r,s),
\end{align*}
where $G$ is a commutative semigroup, $\theta : G^{4} \rightarrow \mathbb{R}_{k}$ a function and $f,g,h$ are functionals on $G^{2}$.
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References
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