In this paper we establish Hyers-Ulam-Rassias stability of a generalized functional equation in fuzzy Banach spaces. The concept originated from Th. M. Rassias theorem that appeared his paper: On the linear mapping spaces, Proc. Amer. Math. Soc. 72 (1978), 297-30.

We solve the inhomogeneous Chebyshev’s differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Chebyshev’s differential equation.

Abstract In this paper, we unify the system of functional equations defining a multi-quadratic–cubic mapping to single equation. Applying fixed point theorem, study generalized Hyers–Ulam stability mappings. As result, investigate hyperstability mappings in some senses.

We survey the recent results concerning the applications of power series method to the study of Hyers–Ulam stability of differential equations.

In this paper, we investigate the exact and approximate controllability, finite time stability, β–Hyers–Ulam–Rassias stability of a fractional order neutral impulsive differential system. The controllability criteria is incorporated with help fixed point approach. famous generalized Grönwall inequality used to study stability. Finally, main results are verified an example.

We show that generalizations of some (classical) results on the Hyers-Ulam stability of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable.

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...

In this study, we examine the existence and Hyers–Ulam stability of a coupled system generalized Liouville–Caputo fractional order differential equations with integral boundary conditions connection to Katugampola integrals. first third theorems, Leray–Schauder alternative Krasnoselskii’s fixed point theorem are used demonstrate solution. The Banach theorem’s concept contraction mapping is in s...

In the present paper the Hyers-Ulam stability of monomial functional equations for functions defined on a power-associative, power-symmetric groupoid is proved.