Volume 35 • Number 3 • 2012   • A Generalized Mixed Quadratic-Quartic Functional Equation Tian Zhou Xu, John Michael Rassias and Wan Xin Xu Abstract. In this paper, we determine the general solution of the functional equation $ f(kx+y)+f(kx-y)= g(x+y)+ g(x-y)+ h(x) +\tilde{h}(y) $ for fixed integers $k$ with $k \neq 0, \pm 1$ without assuming any regularity condition on the unknown functions $f, g, h, \tilde{h}$. The method used for solving these functional equations is elementary but exploits an important result due to Hosszú. The solution of this functional equation can also be determined in certain type of groups using two important results due to Székelyhidi. The results improve and extend some recent results. 2010 Mathematics Subject Classification: Primary: 39B22, 39B82. Full text: PDF