In this paper, we prove the Hyers–Ulam–Rassias stability of the quadratic mapping in generalized quasi-Banach spaces, and of the quadratic mapping in generalized p-Banach spaces.

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 obtain the general solution and investigate the generalized Hyers-Ulam stability of the new generalized mixed type additive and quadratic functional equation in fuzzy normed space. Mathematics Subject Classification 39B55, 39B52, 39B82

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 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) + = + + + − −

In this paper we define the notions of Ulam-Hyers stability on KST spaces and cwweakly Picard operator for the multivalued operators case in order to establish a relation between these.

In this paper, we establish the generalized Hyers-Ulam stability of Jordan homomorphisms and Jordan derivations between ternary algebras via the generalized Jensen equation rf( sx+ty r ) = sf(x) + tf(y).

In this paper, we establish the Pexiderized stability of coboundaries and cocycles and use them to investigate the Hyers–Ulam stability of some functional equations. We prove that for each Banach algebra A, Banach A-bimodule X and positive integer n,H(A,X) = 0 if and only if the n-th cohomology group approximately vanishes.

We investigate the stability of Pexiderized mappings in Banach modules over a unital Banach algebra. As a consequence, we establish the Hyers–Ulam stability of the orthogonal Cauchy functional equation of Pexider type f 1 (x + y) = f 2 (x) + f 3 (y), x ⊥ y in which ⊥ is the orthogonality in the sense of Rätz.

Using the integrating factor method, this paper deals with the Hyers-Ulam stability of a class of exact differential equations of second order. As a direct application of the main result, we also obtain the HyersUlam stability of a special class of Cauchy-Euler equations of second order. c ©2016 All rights reserved.