Geodesic
A Generalized Mixed Quadratic-Quartic Functional Equation
Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 3 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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.
Classification : Primary: 39B22, 39B82. 
@article{BMMS_2012_35_3_a4,
     author = {Tian Zhou Xu and John Michael Rassias and Wan Xin Xu},
     title = {A {Generalized} {Mixed} {Quadratic-Quartic} {Functional} {Equation}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2012},
     volume = {35},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2012_35_3_a4/}
}
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Tian Zhou Xu; John Michael Rassias; Wan Xin Xu. A Generalized Mixed Quadratic-Quartic Functional Equation. Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2012_35_3_a4/