scholarly journals Stability and Superstability of Generalized (, )-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
M. Eshaghi Gordji ◽  
M. B. Ghaemi ◽  
G. H. Kim ◽  
Badrkhan Alizadeh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Generalized Derivation ◽  
Additive Mapping ◽  
Generalized Derivations ◽  
Cauchy Functional Equation ◽  
Cauchy’S Functional Equation ◽  
Additive Cauchy Functional Equation

Let be an algebra, and let , be ring automorphisms of . An additive mapping is called a -derivation if for all . Moreover, an additive mapping is said to be a generalized -derivation if there exists a -derivation such that for all . In this paper, we investigate the superstability of generalized -derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy’s functional equation.

scholarly journals Modelling the Additive Functional Equations through RSM Matrices

2016 ◽  
Vol 12 (10) ◽  
pp. 6714-6719
Author(s):  
Pasupathi Narasimman ◽  
K Ravi ◽  
Sandra Pinelas
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Additive Functional ◽  
Identity Matrix ◽  
Eigenvalues And Eigenvectors ◽  
Cauchy Functional Equation ◽  
Numerical Examples ◽  
Additive Type ◽  
New Type ◽  
Additive Cauchy Functional Equation

This paper suggests one possible method to model additive type of functional equations using eigenvalues and eigenvectors of matrices with suitable numerical examples. The authors have defined a new type of Row Sum Matrix(RSM) and have discussed its eigenvalues and eigenvectors in order to model functional equations. The famous additive cauchy functional equation and Logical functional equation have also been modelled using identity matrix and Logical matrix in this study.

scholarly journals Probabilistic (Quasi)metric Versions for a Stability Result of Baker

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Dorel Miheţ ◽  
Claudia Zaharia
Keyword(s):  
Functional Equation ◽  
Stability Result ◽  
Fixed Point Method ◽  
Normed Spaces ◽  
Cauchy Functional Equation ◽  
Triangular Norms ◽  
Random Normed Spaces ◽  
The Stability ◽  
Probabilistic Metric ◽  
Additive Cauchy Functional Equation

By using the fixed point method, we obtain a version of a stability result of Baker in probabilistic metric and quasimetric spaces under triangular norms of Hadžić type. As an application, we prove a theorem regarding the stability of the additive Cauchy functional equation in random normed spaces.

scholarly journals On Hyperstability of the Cauchy Functional Equation in n-Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1886
Author(s):  
Janusz Brzdęk ◽  
El-sayed El-hady
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Main Tool ◽  
Normed Spaces ◽  
Cauchy Functional Equation ◽  
Additive Cauchy Functional Equation

We present some hyperstability results for the well-known additive Cauchy functional equation f(x+y)=f(x)+f(y) in n-normed spaces, which correspond to several analogous outcomes proved for some other spaces. The main tool is a recent fixed-point theorem.

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