creative_2019_28_1_91_95In this paper, we prove the Hyers-Ulam stability and the
Hyers-Ulam-Rassias stability of the following two functional equations
![\begin{equation*} \varphi (x)=x\varphi ((1-\alpha )x+\alpha )+(1-x)\varphi ((1-\beta )x),\text{ }x\in \lbrack 0,1],\text{ }0<\alpha \leq \beta <1, \end{equation*}](https://www.creative-mathematics.cunbm.utcluj.ro/wp-content/ql-cache/quicklatex.com-0a5cc31b223ba0a1fb077fcf2a1e5cc5_l3.png "Rendered by QuickLaTeX.com")
and
![\begin{equation*} \varphi (x)=x\varphi (f(x))+(1-x)\varphi (g(x)),\text{ }x\in \lbrack 0,1] \end{equation*}](https://www.creative-mathematics.cunbm.utcluj.ro/wp-content/ql-cache/quicklatex.com-1706cb1bf02d8cc479bdd88cf4562730_l3.png "Rendered by QuickLaTeX.com")
which is an open problem raised by Berinde and Khan [Berinde, V. and Khan, A. R., On a functional equation
arising in mathematical biology and theory of learning, Creat. Math. Inform., 24 (2015), No. 1, 9–16].
| Author(s) | Arisoy, Hakan, Kalkan, Zeynep, Şahin, Aynur |
|---|
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