Abstract
Abstract In this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the form f ( 3 x + y ) − 5 f ( 2 x + y ) + f ( 2 x − y ) + 10 f ( x + y ) − 5 f ( x − y ) = 10 f ( y ) + 4 f ( 2 x ) − 8 f ( x ) $$f\left( {3x + y} \right) - 5f\left( {2x + y} \right) + f\left( {2x - y} \right) + 10f\left( {x + y} \right) - 5f\left( {x - y} \right) = 10f\left( y \right) + 4f\left( {2x} \right) - 8f\left( x \right)$$ in the set of real numbers.
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