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

In this paper, we establish the conditional Hyers-Ulam-Rassias stability of the generalized Jensen functional equation r f ( sx+ty r ) = s g(x) + t h(y) on various restricted domains such as inside balls, outside balls, and punctured spaces. In addition, we prove the orthogonal stability of this equation and study orthogonally generalized Jensen mappings on Balls in inner product spaces.

In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C-ternary ring homomorphisms associted to the Trif functional equation d · C d−2f( x1 + · · ·+ xd d ) + C d−2 d ∑

We prove the generalized Hyers-Ulam-Rassias stability of a partitioned functional equation. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with partitioned functional equations in Banach algebras.

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) + = + + + − −

The generalized Hyers–Ulam–Rassias stability of adjointable mappings on Hilbert C∗-modules is investigated. As a corollary, we establish the stability of the equation f(x)∗y = xg(y)∗ in the context of C∗-algebras.

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $mathcal{L}$-fuzzy normed spaces.

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the generalized radical cubic functional equation[    fleft( sqrt[3]{ax^3 + by^3}right)=af(x) + bf(y),]    where $a,b in mathbb{R}_+$ are fixed positive real numbers, by using direct method in quasi-$beta$-Banach spaces. Moreover, we use subadditive functions to investigate stability of the generaliz...

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. ...

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functional equation f(x+ y) + f(x− y) = 2f(x) + 2f(y) in non-Archimedean L-fuzzy normed spaces.