On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

The Hyers-Ulam stability problems of functional equations go back to 1940 when S. M. Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group see 1 . A partial answer was given by Hyers et al. 2, 3 under the assumption that the target space of the involved mappings is a Banach space. After the result of Hyers, Aoki 4 , and Bourgin 5, 6 dealt with this pro...

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...

Generalized Hyers–ulam Stability of Refined Quadratic Functional Equations

In this paper, we give a general solution of a refined quadratic functional equation and then investigate its generalized Hyers–Ulam stability in quasi-normed spaces and in non-Archimedean normed spaces. AMS Subject Classification: 39B82, 39B62

Hyers-Ulam Stability of Fibonacci Functional Equation

On the Hyers-ulam Stability of Quadratic Functional Equations

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability for quadratic functional equations f(2x+ y)+ f(2x− y) = f(x+ y)+ f(x− y)+6f(x) and f(2x + y) + f(x + 2y) = 4f(x + y) + f(x) + f(y).