# Stability of Mappings of Hyers-Ulam Type (Hadronic Press Collection of Original Articles)

• 160 Pages
• 1.56 MB
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Differential Equations, Mathematical Physics, Nonlinear Programming, Mathematics, Science/Mathem
The Physical Object ID Numbers Contributions Jozef Tabor (Editor) Format Hardcover Open Library OL9309598M ISBN 10 0911767827 ISBN 13 9780911767827

Using the fixed point method, we prove the Hyers–Ulam stability of homomorphisms in complex Banach algebras and complex Banach Lie algebras and also of derivations on complex Banach algebras and complex Banach Lie algebras for the general Jensen-type functional equation f(α x + β y) + f(α x − β y) = 2α f(x) for any {\alpha, \beta \in Cited by: 2.

The notion of ψ-additive mappings was first introduced by George Isac related to the asymptotic derivative of mappings. Hyers–Ulam stability of those mappings was studied by G. Isac, Th.M. Rassias Cited by: 1.

### Description Stability of Mappings of Hyers-Ulam Type (Hadronic Press Collection of Original Articles) PDF

Abstract. In this paper, we give an introduction to the Hyers–Ulam–Rassias stability of orthogonally additive mappings. The concept of Hyers–Ulam–Rassias stability originated from Th.M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc.

Math. Soc. –, Our results generalize Cited by: 1. Using the fixed point method, this article proves the Hyers-Ulam-Rassias stability of a generalized Apollonius type quadratic functional equation in Banach spaces.

In this paper, we prove the Hyers-Ulam-Rassias stability and Hyers-Ulam stability of nonlinear delay differential equation with Lipschitz condition by using fixed point approach. The results of the paper generalize most of the results concerning the stability of delay differential equations in the existing literature.

This book is an outcome of two Conferences on Ulam Type Stability (CUTS) organized in (JulyCluj-Napoca, Romania) and in (October, Timisoara, Romania). It presents up-to-date. As an application, we establish the generalized Hyers-Ulam stability theorem on amenable monoids and when σ is an involutive automorphism of S.

Additive Cauchy Equation (Behavior of additive functions, Hyers-Ulam stability, Hyers-Ulam-Rassias stability, Stability on a restricted domain, Method of invariant means, Fixed point method.

the "Hyers-Ulam-Rassias stability" was used in Partial Differential equations was in. Hyers-Ulam-Rassias stability" was used in Ordinary Differential Equations in the papers (,).Cited by: 1. The aim of the present paper is to investigate the Hyers-Ulam stability of the Pexiderized quadratic functional equation, namely of f(x + y)+f (x − y) = 2g(x) + 2h(y) in paranormed spaces.

We are going to show that the generalized Apollonius type quadratic functional equation () is quadratic, and prove the Hyers–Ulam stability of generalized Apollonius type quadratic map- pings in Banach spaces.

Hyers–Ulam stability of a generalized Apollonius type quadratic mapping Throughout this section, Cited by: Keywords: Hyers–Ulam stability; Quadratic mapping of Apollonius type 1. Introduction The stability problem of functional equations originated from a question of S.M.

Ulam [21] concerning the stability of group homomorphisms: Let (G1,∗) be a group and let (G2,d)be Supported by Korea Research Foundation Grant KRFC The first answer to the question of Ulam [2] was given by Hyers in in the case of Banach spaces.

Thereafter, this type of stability is called the Ulam–Hyers stability. InRassias [3] provided a remarkable generalization of the Ulam–Hyers stability of mappings Cited by: We prove the generalized Hyers–Ulam–Rassias stability of generalized A-quadratic mappings of type (P) in Banach modules over a Banach ∗-algebra, and of generalized A-quadratic mappings of type (R) in Banach modules over a Banach ∗ by:   InJung investigated the Hyers-Ulam stability for additive and quadratic mappings on restricted domains (see also [40–42]).

Rassias investigated the Hyers-Ulam stability of mixed type mappings on restricted domains. In, the authors considered the asymptoticity of Hyers-Ulam stability close to the asymptotic by: 5. The concept of generalized Hyers–Ulam–Rassias stability originated from Th.

Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72, –, Author: Fridoun Moradlou, Themistocles M. Rassias. Hyers-Ulam stability of an Euler-Lagrange type additive mapping.

Journal of Mathematical Analysis and Applications] doirjmaa, available online at http: on A Generalization of the Hyers]Ulam]Rassias Stability of the Pexider Equation Yang-Hi Lee 1 Department of Mathematics Education, Kongju National Unicurrency1ersity of Education, KongjuCited by: In this paper we prove a fixed-point theorem for a class of operators with suitable properties, in very general conditions.

Also, we show that some recent fixed-points results in Brzdęk et al., () and Brzdęk and Ciepliński () can be obtained directly from our theorem. Moreover, an affirmative answer to the open problem of Brzd&#x;k and Ciepli&#x;ski () is by: We also have proved the Hyers-Ulam stability of Emden-Fowler type equation with initial conditions.

Introduction. In Ulam posed the basic problem of the stability of functional equations: Give conditions in order for a linear mapping near an approximately linear mapping Cited by: 3.

We prove a general result on Ulam's type stability of the functional equation f(x + y) = f(x) + f(y), in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability by: 2. In the present paper we study the generalized Hyers–Ulam stability of the generalized trigonometric functional equations f (x y) + μ (y) f (x σ (y)) = 2 f (x) g (y) + 2 h (y), x, y ∈ S ; f (x y) + μ (y) f (x σ (y)) = 2 f (y) g (x) + 2 h (x), x, y ∈ S, where S is a semigroup, σ: S S is a involutive morphism, and μ: S C is a multiplicative Cited by: 1.

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2,xn + yn) = f(x1, x2, xn) + f(y1, y2,yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the Author: Yang-Hi Lee, Gwang Hui Kim.

ONTHEHYERS–ULAM STABILITY OF SEXTIC FUNCTIONAL EQUATIONS [37] ANDY. C HO,Stability of mixed additive-quadratic Jensen type functional equation in various spaces, Appl.

61 (), – [38] M. KHAMSI, Quasicontraction Mapping in modular spaces without Δ2 –condition, Fixed Point Theory Appl. provided a lot of inﬂuence in the development of a generalization of the Hyers–Ulam stabil-ity concept.

### Details Stability of Mappings of Hyers-Ulam Type (Hadronic Press Collection of Original Articles) PDF

This new concept is known as Hyers–Ulam–Rassias stability of functional equations (cf. the books of P. Czerwik [4] and D.H. Hyers, G. Isac and Th.M. Rassias [8]). Hyers-Ulam-Rassias Stability of n-Apollonius Type Additive Mapping and Isomorphisms in C∗-Algebras Fridoun Moradlou Department of Mathematics Sahand University of Technology, Tabriz, Iran [email protected] Choonkil Park Department of Mathematics, Hanyang University Seoul, –, Republic of Korea [email protected] Jung Rye Lee.

Let X,Y be linear spaces. It is shown that if a mapping satisfies the following functional equation: then the mapping is quadratic. We moreover prove the Hyers-Ulam stability of the functional equation () in Banach spaces.

The stability problem of functional equations was originated from a question of Ulam [] concerning the stability of group be a group and let be a metric group with thedoes there exist a such that, if a function satisfies the inequality for all, then there exists a homomorphism with for all.

In other words, we are looking for Cited by: Recently, Jung presented a book, which complements the books of Hyers, Isac, and Rassias (Stability of Functional Equations in Several Variables, Birkhäuser, ) and of Czerwik (Functional Equations and Inequalities in Several Variables, World Scientific, ) by covering and offering almost all classical results on the Hyers-Ulam-Rassias Cited by: The results in Theorems 2, 4, and 5 have been extended in, where a result on the generalized Hyers-Ulam stability of the nonlinear equation has been obtained, also by the weighted space method.

Here, is a nonempty set, is a complete metric space, and are given mappings (the unknown function in is). Theorem 6 (, Theorem 2).Cited by:.

Aoki and Gajda proved the generalized Hyers-Ulam stability for an additive mapping in the cases where 0 ≤ p stability for an additive mapping does not holds for the case p ≠ : Yang-Hi Lee, Gwang-Hui Kim.On the Stability of Functional Equations in Banach Spaces The paper is devoted to some results on the problem of S.

M. Ulam for the stability of functional equations in Banach spaces. The problem was posed by Ulam 60 years ago. (Eds.), Stability of Mappings of Hyers–Ulam Type, Hadronic Press (), pp. Google Scholar. 7. P.W Cited by: Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis Soon-Mo Jung (auth.) This textbook at the advanced undergraduate/graduate level will complement the books of D.H.

Hyers, G.