A General Fixed Point Method for the Stability of Cauchy Functional Equation

2011 ◽  
pp. 19-32 ◽  
Author(s):  
Liviu Cădariu ◽  
Viorel Radu
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Cauchy Functional Equation ◽  
The Stability

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

scholarly journals Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

scholarly journals The Stability of a Quadratic Functional Equation with the Fixed Point Alternative

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Choonkil Park ◽  
Ji-Hye Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
The Stability

Lee, An and Park introduced the quadratic functional equationf(2x+y)+f(2x−y)=8f(x)+2f(y)and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.

The stability of a connection on Hermitian vector bundles over a Riemannian manifold

2016 ◽  
Vol 09 (01) ◽  
pp. 1650001
Author(s):  
Rohollah Bakhshandeh-Chamazkoti ◽  
Mehdi Nadjafikhah
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Riemannian Manifold ◽  
Vector Bundles ◽  
Fixed Point Method ◽  
Point Method ◽  
The Stability ◽  
Rassias Stability ◽  
Hermitian Vector Bundles

In this attempt, the stability of a connection on Hermitian vector bundles over a Riemannian manifold for the generalized Jensen-type functional equation [Formula: see text] is discussed. In fact, the main purpose of this paper is to prove the generalized Hyers–Ulam–Rassias stability of connection on between Hermitian [Formula: see text] and [Formula: see text]. Also we will use the fixed point method to prove the stability of this connection for the above generalized Jensen-type functional equation.

scholarly journals On the Generalized Hyers–Ulam Stability of a Functional Equation and Its Consequences

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Krzysztof Ciepliński
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
The Stability

AbstractThe aim of this note is to show the generalized Hyers–Ulam stability of a functional equation in four variables. In order to do this, the fixed point method is applied. As corollaries from our main result, some outcomes on the stability of some known equations will be also derived.

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