Abstract
In this article, we obtain a characterizations and representations of set-valued solutions defined on an Abelian group G with values in a Hausdorff topological vector space of the following generalized biquadratic functional equation:
F(x + y, z + w) + F(x + y, z - w) + F(x - y, z + w) + F(x - y, z - w) = aF(x, z) + bF (x, w) + cF (y, z) + dF(y, w),
for some nonnegative real numbers a, b, c, and d.