In this paper, we establish the general solution of the functional equation f(nx+ y) + f(nx− y) = nf(x+ y) + nf(x− y) + 2(f(nx)− nf(x))− 2(n − 1)f(y) for fixed integers n with n 6= 0,±1 and investigate the generalized Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces.

In this paper, we present the HyersUlamRassias stability of quartic functional equation f(2x + y) + f(2x – y) = 4.f(x + y) + 4f(x – y) + 24f(x) ( 6f(y) in Random 2Normed space . References 1. A. Alotaibi, S.A. Mohiuddine; On the stability of a cubic functional equation in random 2-normed spaces, Advances in Difference Equations, 1,39 (2012) pp. 1-10. 2. D.H. Hyers; On the stability of the linea...

We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.

The generalized Hyers-Ulam-Rassias stability proposition in respect of the quadratic functional equation namely f(x+y+z)+f(x−y)+f(x−z) = f(x−y−z)+f(x+y)+f(x+z) is what is taken into account to be dealt with in this paper.

In this paper, we prove the generalized Hyres–Ulam–Rassias stability of the mixed type cubic and quartic functional equation f (x + 2y) + f (x − 2y) = 4(f (x + y) + f (x − y)) − 24f (y) − 6f (x) + 3f (2y) in non-Archimedean ℓ-fuzzy normed spaces.

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation 3(f(x+ 2y) + f(x− 2y)) = 12(f(x + y) + f(x− y)) + 4f(3y)− 18f(2y) + 36f(y)− 18f(x).

We investigate the following generalized Cauchy functional equation f(αx+ βy) = αf(x) + βf(y) where α, β ∈ R \ {0}, and use a fixed point method to prove its generalized Hyers–Ulam–Rassias stability in Banach modules over a C∗-algebra.

in this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and also investigate the hyers-ulam-rassiasstability of n-jordan *-homomorphisms on c*-algebras.