ON HYPERSTABILITY OF GENERALISED LINEAR FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES

2015 ◽  
Vol 92 (2) ◽  
pp. 259-267 ◽  
Author(s):  
DONG ZHANG
Keyword(s):  
Functional Equation ◽  
Exact Solutions ◽  
Normed Space ◽  
Functional Equations ◽  
Linear Functional ◽  
Approximate Solutions ◽  
Linear Functional Equation ◽  
Several Variables ◽  
Linear Functional Equations

We obtain some results on approximate solutions of the generalised linear functional equation $\sum _{i=1}^{m}L_{i}f(\sum _{j=1}^{n}a_{ij}x_{j})=0$ for functions mapping a normed space into a normed space. We show that, under suitable assumptions, the approximate solutions are in fact exact solutions. The theorems correspond to and complement recent results on the hyperstability of generalised linear functional equations.

scholarly journals Stability of linear functional equations in Banach modules

2004 ◽  
Vol 35 (1) ◽  
pp. 29-36
Author(s):  
Chun-Gil Park
Keyword(s):  
Functional Equation ◽  
Banach Algebra ◽  
Functional Equations ◽  
Linear Functional ◽  
Linear Functional Equation ◽  
Linear Functional Equations ◽  
Banach Modules ◽  
Unital Banach Algebra ◽  
Rassias Stability

We prove the Hyers-Ulam-Rassias stability of the linear functional equation in Banach modules over a unital Banach algebra.

HYPERSTABILITY OF GENERALISED LINEAR FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES

2020 ◽  
Vol 102 (2) ◽  
pp. 293-302
Author(s):  
THEERAYOOT PHOCHAI ◽  
SATIT SAEJUNG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
Linear Functional ◽  
Linear Equations ◽  
General Linear ◽  
Several Variables ◽  
Linear Functional Equations

Zhang [‘On hyperstability of generalised linear functional equations in several variables’, Bull. Aust. Math. Soc.92 (2015), 259–267] proved a hyperstability result for generalised linear functional equations in several variables by using Brzdęk’s fixed point theorem. We complete and extend Zhang’s result. We illustrate our results for general linear equations in two variables and Fréchet equations.

scholarly journals Solution of a Nonlinear Functional Equation

2004 ◽  
Vol 9 ◽  
pp. 25
Author(s):  
Valery C. Covachev ◽  
H. Ali Yurtsever
Keyword(s):  
Functional Equation ◽  
Matrix Method ◽  
Functional Equations ◽  
Linear Functional ◽  
Parametric Approach ◽  
Nonlinear Functional Equation ◽  
Nonlinear Functional ◽  
Linear Functional Equations

In the present paper a generalization of a theorem of I.B. Risteski (2004) concerning the solution of a nonlinear functional equation is given. The proof is based on a parametric approach by introducing a parameter in an arbitrary set , and on a matrix method for solving linear functional equations. 

scholarly journals Stability of Functional Equations in Dislocated Quasi-Metric Spaces

2018 ◽  
Vol 32 (1) ◽  
pp. 215-225 ◽  
Author(s):  
Beata Hejmej
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Linear Functional ◽  
Metric Spaces ◽  
Linear Functional Equation ◽  
Ulam Stability ◽  
Cauchy Functional Equation ◽  
Complete Metric Spaces ◽  
Stability Of Functional Equations ◽  
Quasimetric Space

Abstract We present a result on the generalized Hyers-Ulam stability of a functional equation in a single variable for functions that have values in a complete dislocated quasi-metric space. Next, we show how to apply it to prove stability of the Cauchy functional equation and the linear functional equation in two variables, also for functions taking values in a complete dislocated quasimetric space. In this way we generalize some earlier results proved for classical complete metric spaces.

scholarly journals Applications of Banach Limit in Ulam Stability

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 841
Author(s):  
Roman Badora ◽  
Janusz Brzdęk ◽  
Krzysztof Ciepliński
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Linear Functional ◽  
Linear Functional Equation ◽  
Ulam Stability ◽  
Single Variable ◽  
Cauchy Equation ◽  
Banach Limit

We show how to get new results on Ulam stability of some functional equations using the Banach limit. We do this with the examples of the linear functional equation in single variable and the Cauchy equation.

Oscillation analysis of solutions of non-zero continuous linear functional equations

2021 ◽  
pp. 1-11
Author(s):  
Nan Yin
Keyword(s):  
Functional Equations ◽  
Linear Functional ◽  
Sufficient Conditions ◽  
Theory And Practice ◽  
Linear Functional Equation ◽  
Continuous Linear ◽  
Continuous Linear Functional ◽  
Oscillation Analysis ◽  
Linear Functional Equations ◽  
Oscillation Characteristics

As a mathematical model of mechanical and electronic oscillation, the study and analysis of the oscillation characteristics of the solution of the non-zero continuous linear functional equation are of great significance in theory and practice. In view of the oscillation characteristics of the solutions of the second and third order non-zero continuous functional equations, this paper puts forward a hypothesis, studies the oscillation and asymptotics of the non-zero continuous linear functional differential equations by using the generalized Riccati transformation and the integral average technique, and establishes some new sufficient conditions for the oscillation or convergence to zero of all solutions of the equations, so as to obtain a new theorem for the solutions of the non-zero continuous linear functional equations.

scholarly journals The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 174-192
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Group ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

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