Fixed Point Methods for the Generalized Stability of Functional Equations in a Single Variable

By Liviu Cadariu, Viorel Radu. 2007

172 citations recorded by the source corpus.

We discuss on the generalized Ulam-Hyers stability for functional equations in a single variable, including the nonlinear functional equations, the linear functional equations, and a generalization of functional equation for the square root spiral. The stability results have been obtained by a fixed point method. This method introduces a metrical context and shows that the stability is related to some fixed point of a suitable operator.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6aed0338ffcf825772a01c6b2506b8c1db296ff8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Janusz Brzdek
2. Michael Th. Rassias
3. Soon-Mo Jung
4. Krzysztof Cieplinski
5. Ioan A. Rus
6. Mohammad Sal Moslehian
7. Liviu Cadariu
8. Akbar Zada

In Geometry and Topology

1. Soon-Mo Jung
2. Janusz Brzdek
3. Michael Th. Rassias

Citations in the corpus

• A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers (2014, background): “For further discussion and references one is referred to [5, 6, 7, 23, 30].”
• Hyperstability of the Cauchy equation on restricted domains (2013, methodology): “The fixed point results have been already used for proving stability of functional equation for instance in [2,9,28–30,34,35] and our method can be considered to be an extension of those investigations (for a survey on this subject see [10]).”