On the Generalized Hyers-Ulam Stability of a Cauchy-Jensen Functional Equation

Hyers-Ulam Stability of Fibonacci Functional Equation

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) + = + + + − −

Hyers-Ulam stability of a generalized trigonometric-quadratic functional equation

The Hyers-Ulam stability of the generalized trigonometric-quadratic functional equation ( ) ( ) ( ) ( ) ( ) ( ) 2 F x y G x y H x K y L x M y + − − = + + over the domain of an abelian group and the range of the complex field is established based on the assumption of the unboundedness of the function K. Subject to certain natural conditions, explicit shapes of the functions H and K are determine...

Hyers–ulam–rassias Stability of a Generalized Pexider Functional Equation

In this paper, we obtain the Hyers–Ulam–Rassias stability of the generalized Pexider functional equation ∑ k∈K f(x+ k · y) = |K|g(x) + |K|h(y), x, y ∈ G, where G is an abelian group, K is a finite abelian subgroup of the group of automorphism of G. The concept of Hyers–Ulam–Rassias stability originated from Th.M. Rassias’ Stability Theorem that appeared in his paper: On the stability of the lin...

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...