Abstract
In this paper, we establish the general solution and the generalized Hyers–Ulam–Rassias stability problem for a cubic Jensen–type functional equation, $$ \begin{aligned} & 4f{\left( {\frac{{3x + y}} {4}} \right)} + 4f{\left( {\frac{{x + 3y}} {4}} \right)} = 6f{\left( {\frac{{x + y}} {2}} \right)} + f{\left( x \right)} + f{\left( y \right)}, \\ & 9f{\left( {\frac{{2x + y}} {3}} \right)} + 9f{\left( {\frac{{x + 2y}} {3}} \right)} = 16f{\left( {\frac{{x + y}} {2}} \right)} + f{\left( x \right)} + f{\left( y \right)} \\ \end{aligned} $$ in the spirit of D. H. Hyers, S. M. Ulam, Th. M. Rassias and P. Găvruta.
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