Hyers—Ulam stability of functional equations in several variables

1995 ◽  
pp. 143-190
Author(s):  
Gian Luigi Forti
Keyword(s):  
Functional Equations ◽  
Ulam Stability ◽  
Several Variables ◽  
Stability Of Functional Equations

scholarly journals Ulam stability of functional equations in 2-Banach spaces via the fixed point method

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Krzysztof Ciepliński
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Several Variables ◽  
Stability Of Functional Equations ◽  
Special Cases ◽  
The Stability

AbstractUsing the fixed point method, we prove the Ulam stability of two general functional equations in several variables in 2-Banach spaces. As corollaries from our main results, some outcomes on the stability of a few known equations being special cases of the considered ones will be presented. In particular, we extend several recent results on the Ulam stability of functional equations in 2-Banach spaces.

scholarly journals A General Uniqueness Theorem concerning the Stability of Additive and Quadratic Functional Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Uniqueness Theorem ◽  
Functional Equations ◽  
Additive Functional ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Additive Type ◽  
Stability Of Functional Equations ◽  
The Stability

We prove a general uniqueness theorem that can be easily applied to the (generalized) Hyers-Ulam stability of the Cauchy additive functional equation, the quadratic functional equation, and the quadratic-additive type functional equations. This uniqueness theorem can replace the repeated proofs for uniqueness of the relevant solutions of given equations while we investigate the stability of functional equations.

scholarly journals On a general Hyers-Ulam stability result

1995 ◽  
Vol 18 (2) ◽  
pp. 229-236 ◽  
Author(s):  
Costanz Borelli ◽  
Gian Luigi Forti
Keyword(s):  
Functional Equations ◽  
Stability Result ◽  
Quadratic Equation ◽  
Ulam Stability ◽  
Stability Of Functional Equations ◽  
The Stability

In this paper, we prove two general theorems about Hyers-Ulam stability of functional equations. As particular cases we obtain many of the results published in the last ten years on the stability of the Cauchy and quadratic equation.

scholarly journals On Ulam Stability of Functional Equations in 2-Normed Spaces—A Survey

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2200
Author(s):  
Anna Bahyrycz ◽  
Janusz Brzdęk ◽  
El-sayed El-hady ◽  
Zbigniew Leśniak
Keyword(s):  
Exact Solutions ◽  
Approximation Theory ◽  
Functional Equations ◽  
Approximate Solutions ◽  
Main Issue ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Stability Of Functional Equations

The theory of Ulam stability was initiated by a problem raised in 1940 by S. Ulam and concerning approximate solutions to the equation of homomorphism in groups. It is somehow connected to various other areas of investigation such as, e.g., optimization and approximation theory. Its main issue is the error that we make when replacing functions satisfying the equation approximately with exact solutions of the equation. This article is a survey of the published so far results on Ulam stability for functional equations in 2-normed spaces. We present and discuss them, pointing to the various pitfalls they contain and showing possible simple generalizations. In this way, in particular, we demonstrate that the easily noticeable symmetry between them and the analogous results obtained for the classical metric or normed spaces is in fact only apparent.

scholarly journals Stability of Functional Equations and Properties of Groups

2019 ◽  
Vol 33 (1) ◽  
pp. 77-96
Author(s):  
Gian Luigi Forti
Keyword(s):  
Additive Function ◽  
Functional Equations ◽  
Ulam Stability ◽  
Cauchy Equation ◽  
Stability Of Functional Equations ◽  
The Given

AbstractInvestigating Hyers–Ulam stability of the additive Cauchy equation with domain in a group G, in order to obtain an additive function approximating the given almost additive one we need some properties of G, starting from commutativity to others more sophisticated. The aim of this survey is to present these properties and compare, as far as possible, the classes of groups involved.

Sign in / Sign up

Export Citation Format

Share Document