In the paper we discuss a stability in the sense of the generalized Hyers-Ulam-Rassias for functional equations ∆n(p, c)φ(x) = h(x), which is called generalized Newton difference equations, and give a sufficient condition of the generalized Hyers-Ulam-Rassias stability. As corollaries, we obtain the generalized Hyers-Ulam-Rassias stability for generalized forms of square root spirals functional...

The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ theoremwas generalized byAoki 3 for additive mappings and by Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Rassias 4 has pr...

The stability problem of functional equations is originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ Theorem was generalized by Aoki 3 for additive mappings and by Th. M. Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Th. ...

In this paper, we investigate four different types of Ulam stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of nonlinear implicit fractional differential equations with non-instantaneous integral impulses and nonlinear integral boundary condition. We also establish certain conditions fo...

Recently, in [5], Najati and Moradlou proved Hyers-Ulam-Rassias stability of the following quadratic mapping of Apollonius type Q(z − x) + Q(z − y) = 1 2 Q(x− y) + 2Q ( z − x + y 2 ) in non-Archimedean space. In this paper we establish Hyers-Ulam-Rassias stability of this functional equation in random normed spaces by direct method and fixed point method. The concept of Hyers-Ulam-Rassias stabi...

In this paper,we consider functional equations involving a two variables examine some of these equations in greater detail and we study applications of cauchy’s equation.using the generalized hyers-ulam-rassias stability of quaradic functional equations finding the solution of two variables(quaradic functional equations) 1.INTRODUCTION We achieve the general solution and the generalized Hyers-U...

The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ theorem was generalized by Aoki 3 for additive mappings and by Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Rassias 4 has ...

The stability problem of the functional equation was conjectured by Ulam 1 during the conference in the University of Wisconsin in 1940. In the next year, it was solved by Hyers 2 in the case of additive mapping, which is called the Hyers-Ulam stability. Thereafter, this problem was improved by Bourgin 3 , Aoki 4 , Rassias 5 , Ger 6 , and Gǎvruţa et al. 7, 8 in which Rassias’ result is called t...

In this paper we present four types of Ulam stability for ordinary differential equations: Ulam-Hyers stability, generalized UlamHyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-HyersRassias stability. Some examples and counterexamples are given.

In this paper, we investigate the generalized Hyers Ulam Rassias stability of a new quadratic functional equation f(2x + y) + f(2x− y) = 2f(x + y) + 2f(x− y) + 4f(x)− 2f(y). Generalized Hyers-Ulam-Rassias Stability K. Ravi, R. Murali and M. Arunkumar vol. 9, iss. 1, art. 20, 2008 Title Page