Mixed Type Of Additive And Quintic Functional Equations

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(3x+y)−5f(2x+y)+f(2x−y)+10f(x+y)−5f(x−y)=10f(y)+4f(2x)−8f(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.