Stability of a quartic functional equation

In this paper, the authors investigate the general solution and generalized Hyers–Ulam stability of the n-dimensional quartic functional equation of the form f(∑i=1nxi)=∑1≤i<j<k<l≤nf(xi+xj+xk+xl)+(-n+4)∑1≤i<j<k≤nf(xi+xj+xk)+(n2-7n+122)∑1=i;i≠jnf(xi+xj)-∑i=1nf(2xi)+(-n3+9n2-26n+1206)∑i=1n(f(xi)+f(-xi)2)where n is a positive integer with N- { 0 , 1 , 2 , 3 , 4 }. The stability of this quartic functional equation is introduced in Banach space using direct and fixed point methods. © 2018, Springer Nature Switzerland AG.