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...

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 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’ 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 ...

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...

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 Th. M. Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Th. M. ...

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 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982–2005 we established the Hyers–Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1998 S.-M. Jung and in 2002–2005 the authors of this paper investigated the Hyers–Ulam stability of additive ...

in this paper, using the fixed point and direct methods, we prove the generalized hyers-ulam-rassias stability of the following cauchy-jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. the concept of hyers-ulam-rassias stability originated from th. m. rassias’ stability theorem t...