Received Okt 2, 2014 Revised Nov 1, 2014 Accepted Nov 23, 2014 In this paper, a generalization to nonlinear systems is proposed and applied to the motordynamic, rotor model and stator model in DC motor equation. We argue that Ulam-Hyers stability concept is quite significant in design problems and in design analysis for the class of DC motor’s parameters. We prove the stability of nonlinear par...

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. ...

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 ...

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...

This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem  is used for obtaining  existence and uniqueness of solutions. By means of   abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish  Hyers-Ulam stabi...

The functional equation f(3x) = 4f(3x−3)+f(3x− 6) will be solved and its Hyers-Ulam stability will be also investigated in the class of functions f : R → X , where X is a real Banach space. Keywords—Functional equation, Lucas sequence of the first kind, Hyers-Ulam stability.

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. In this paper we introduce generalized additive mappings of Jensen type mappings and establish new theorems about the Ulam stability of additive and alternative additive mappings.

Abstract In this paper, we introduce a new integral transform, namely Aboodh and apply the transform to investigate Hyers–Ulam stability, Hyers–Ulam–Rassias Mittag-Leffler–Hyers–Ulam Mittag-Leffler–Hyers–Ulam–Rassias stability of second order linear differential equations.

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

By using a fixed point method, we establish the Hyers–Ulam stability and the Hyers–Ulam–Rassias stability for a general class of nonlinear Volterra integral equations in Banach spaces. 2000 Mathematics Subject Classification: Primary 45N05, 47J05, 47N20, 47J99, Secondary 47H99, 45D05, 47H10.