In this paper, we define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation: f (x 1 + · · · + x l) = (l – 1)f x 1 + · · · + x l–1 l – 1 + f (x l) for a fixed integer l with l > 1, and prove the Hyers-Ulam stability of the generalized additive set-valued functional equation.

The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation

In this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$  is orthogonality in the sense of Ratz.

For an algebraically closed field k of characteristic 0, we give a cycle-theoretic description of the additive 4-term motivic exact sequence associated to the additive dilogarithm of J.-L. Cathelineau, that is the derivative of the Bloch-Wigner function, via the cubical additive higher Chow groups under one assumption. The 4-term functional equation of Cathelineau, an additive analogue of the A...

in this paper, using the fixed point and direct methods, we prove the generalized hyers-ulam-rassias stability of the following cauchy-jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. the concept of hyers-ulam-rassias stability originated from th. m. rassias’ stability theorem t...