On the Definition of a Quadratic Form
On the existence and uniqueness of integrable solutions of functional equations in Banach space.
On the existence and uniqueness of the solution of a non-linear functional equation of r-th order
On the formal first cocycle equation for iteration groups of type II
Let x be an indeterminate over ℂ. We investigate solutions αn : ℂ → ℂ, n ≥ 0, of the first cocycle equation in ℂ [[x]], the ring of formal power series over ℂ, where (F(s,x))s ∈ ℂ is an iteration group of type II, i.e. it is a solution of the translation equation of the form F(s,x) ≡ x + ck(s)xk mod xk+1, where k ≥ 2 and ck ≠ 0 is necessarily an additive function. It is easy to prove that the coefficient functions αn(s) of are polynomials in ck(s).It is possible to replace...
On the Functional Equation
On the functional equation defined by Lie's product formula
Let E be a real normed space and a complex Banach algebra with unit. We characterize the continuous solutions f: E → of the functional equation .
On the Functional Equation f(m +n - mn) + f(mn) + f(n).
On the functional equation f(x) = ...f((x+j)/k) over finite rings.
On the Functional Equation f(x) = ...f((x+j)/k) Over Finite Rings. (Short Communication).
On the functional equation f(x +f(y)) = f(x)f(y).
On the functional equation f(x + f(y)) = (x) f(y). (Short Communication).
On the functional equation H [tau (F,G), chi (F,G)] = H (F,G).
In this paper we solve the functional equationH [tau(F,G), chi (F,G)] = H (F,G)where the unknowns tau and chi are two semigroups on a space of distribution functions, and H is a given pointwise binary operation on this space satisfying some regularity conditions.
On the Functional Equation of Cauchy.
On the Functional Equation ... (x) + ... (y) = v(T(x, y))
On the general solution of the triangle mean value equation. (Short Communication).
On the general solution of the triangle mean value equation.
On the generalised equations of associativity and bisymmetry.
On the generalized cube and octahedron functional equations.
On the generalized Ulam-Gavruta-Rassias stability of mixed-type linear and Euler-Lagrange-Rassias functional equations.
On the graph of a quasi-additive function.