On the fine spectrum of the generalized difference operator over the sequence spaces and .
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
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 = fg
On the functional equation f = fg.
On the Functional Equation f phi f = f
On the functional equation
On the Functional Equation f (x + t, y) + f (x - t, y) = f (x, y + t) + f (x, y - t).
On the Functional Equation f(m +n - mn) + f(mn) + f(n).
On the Functional Equation f(p + qx + rf (x)) = a + bx + cf (x). (Short Communication).
On the Functional Equation f(p + qx + rf(x)) = a + bx + cf(x).
On the Functional Equation F(u) = F(1 - n) + F(...), ...[0,...]
On the Functional Equation F(u) = F(l - u) + F(u/l - u), u ... [0, ...] (Short Communication)
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 f(x) g(y) = p(x+y) q(x/y).