Hyers-Ulam stability of Butler-Rassias functional equation

Hyers-ulam Stability of Butler-rassias Functional Equation

In 1940, Ulam [9] gave a wide ranging talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of important unsolved problems. Among those was the following question concerning the stability of homomorphisms. Let G1 be a group and let G2 be a metric group with a metric d(·,·). Given ε > 0, does there exist a δ > 0 such that if a function h : G1 → G2 satisfi...

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–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...

Hyers-Ulam Stability of Fibonacci Functional Equation

Hyers-Ulam-Rassias stability of a composite functional equation in various normed spaces

In this paper, we prove the generalized Hyers-Ulam(or Hyers-Ulam-Rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.