Stability problem of Ulam for generalized forms of Cauchy functional equation

Hyers-Ulam Stability of Fibonacci Functional Equation

Generalized Hyers-Ulam Stability of the Pexiderized Cauchy Functional Equation in Non-Archimedean Spaces

The stability problem of functional equations was originated from a question of Ulam 1 concerning the stability of group homomorphisms. Let G1 be a group and let G2 be a metric group with the metric d ·, · . Given > 0, does there exist a δ > 0 such that, if a function h : G1 → G2 satisfies the inequality d h xy , h x h y < δ for all x, y ∈ G1, then there exists a homomorphism H : G1 → G2 with d...

Hyers-Ulam stability of K-Fibonacci functional equation

Let denote by Fk,n the nth k-Fibonacci number where Fk,n = kFk,n−1+Fk,n−2 for n 2 with initial conditions Fk,0 = 0, Fk,1 = 1, we may derive a functionalequation f(k, x) = kf(k, x − 1) + f(k, x − 2). In this paper, we solve thisequation and prove its Hyere-Ulam stability in the class of functions f : N×R ! X,where X is a real Banach space.

Non-Archimedean stability of Cauchy-Jensen Type functional equation

In this paper we investigate the generalized Hyers-Ulamstability of the following Cauchy-Jensen type functional equation$$QBig(frac{x+y}{2}+zBig)+QBig(frac{x+z}{2}+yBig)+QBig(frac{z+y}{2}+xBig)=2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces

Generalized Hyers - Ulam - Rassias Stability of a Quadratic Functional Equation

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of a new quadratic functional equation f (2x y) 4f (x) f (y) f (x y) f (x y) + = + + + − −