Functional equations associated with triangle geometry.
The equation φ (x) = g(x,φ (x)) in spaces of real-analytic functions is considered. Connections between local and global aspects of its solvability are discussed.
Let X be a real linear topological space. We characterize solutions f:X → ℝ and M:ℝ → ℝ of the equation f(x+M(f(x))y) = f(x)f(y) under the assumption that f and M have the Darboux property.