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 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.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

scholarly journals Approximation of additive functional equations in NA Lie C*-algebras

2018 ◽  
Vol 51 (1) ◽  
pp. 37-44 ◽  
Author(s):  
Zhihua Wang ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Additive Functional ◽  
Fixed Point Method ◽  
Content Type ◽  
Additive Functional Equation ◽  
C Algebras ◽  
Stable Map ◽  
Higher Derivation

AbstractIn this paper, by using fixed point method, we approximate a stable map of higher *-derivation in NA C*-algebras and of Lie higher *-derivations in NA Lie C*-algebras associated with the following additive functional equation,where m ≥ 2.

On the stability of some functional equations in Menger φ-normed spaces

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Dorel Miheţ ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
The Stability ◽  
Stability Results

AbstractRecently, the authors [MIHEŢ, D.—SAADATI, R.—VAEZPOUR, S. M.: The stability of an additive functional equation in Menger probabilistic φ-normed spaces, Math. Slovaca 61 (2011), 817–826] considered the stability of an additive functional in Menger φ-normed spaces. In this paper, we establish some stability results concerning the cubic, quadratic and quartic functional equations in complete Menger φ-normed spaces via fixed point theory.

A HYPERSTABILITY RESULT FOR THE CAUCHY EQUATION

2013 ◽  
Vol 89 (1) ◽  
pp. 33-40 ◽  
Author(s):  
JANUSZ BRZDĘK
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Normed Space ◽  
Functional Equations ◽  
Cauchy Equation ◽  
Cauchy Functional Equation ◽  
Real Numbers ◽  
Formula One ◽  
Image Position

AbstractWe prove a hyperstability result for the Cauchy functional equation$f(x+ y)= f(x)+ f(y)$, which complements some earlier stability outcomes of J. M. Rassias. As a consequence, we obtain the slightly surprising corollary that for every function$f$, mapping a normed space${E}_{1} $into a normed space${E}_{2} $, and for all real numbers$r, s$with$r+ s\gt 0$one of the following two conditions must be valid:$$\begin{eqnarray*}\displaystyle \sup _{x, y\in E_{1}}\Vert f(x+ y)- f(x)- f(y)\Vert \hspace{0.167em} \mathop{\Vert x\Vert }\nolimits ^{r} \hspace{0.167em} \mathop{\Vert y\Vert }\nolimits ^{s} = \infty , &&\displaystyle\end{eqnarray*}$$$$\begin{eqnarray*}\displaystyle \sup _{x, y\in E_{1}}\Vert f(x+ y)- f(x)- f(y)\Vert \hspace{0.167em} \mathop{\Vert x\Vert }\nolimits ^{r} \hspace{0.167em} \mathop{\Vert y\Vert }\nolimits ^{s} = 0. &&\displaystyle\end{eqnarray*}$$In particular, we present a new method for proving stability for functional equations, based on a fixed point theorem.

scholarly journals Homomorphisms and Derivations inC*-Algebras

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Choonkil Park ◽  
Abbas Najati
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Additive Functional ◽  
Additive Functional Equation ◽  
Stability Method ◽  
Rassias Stability

Using the Hyers-Ulam-Rassias stability method of functional equations, we investigate homomorphisms inC*-algebras, LieC*-algebras, andJC*-algebras, and derivations onC*-algebras, LieC*-algebras, andJC*-algebras associated with the following Apollonius-type additive functional equationf(z−x)+f(z−y)+(1/2)f(x+y)=2f(z−(x+y)/4).

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.

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