Pexiderization of some logarithmic functional equations

Some Logarithmic Functional Equations

The functional equation f(y − x) − g(xy) = h (1/x− 1/y) is solved for general solution. The result is then applied to show that the three functional equations f(xy) = f(x)+f(y), f(y−x)−f(xy) = f(1/x−1/y) and f(y−x)−f(x)−f(y) = f(1/x−1/y) are equivalent. Finally, twice differentiable solution functions of the functional equation f(y − x) − g1(x) − g2(y) = h (1/x− 1/y) are determined.

Stability of General Newton Functional Equations for Logarithmic Spirals

Generalized Orthogonal Stability of Some Functional Equations

We deal with a conditional functional inequality x ⊥ y ⇒ ‖ f (x + y)− f (x)− f (y) ‖ ≤ (‖ x‖ + ‖ y‖ ), where ⊥ is a given orthogonality relation, is a given nonnegative number, and p is a given real number. Under suitable assumptions, we prove that any solution f of the above inequality has to be uniformly close to an orthogonally additive mapping g, that is, satisfying the condition x ⊥ y ⇒ g(...

Stability theorems for some functional differential equations

Some functional equations originating from number theory

If the answer is affirmative, the functional equation for homomorphisms is said to be stable in the sense of Hyers and Ulam because the first result concerning the stability of functional equations was presented by Hyers. Indeed, he has answered the question of Ulam for the case where G1 and G2 are assumed to be Banach spaces (see [8]). We may find a number of papers concerning the stability re...