scholarly journals Stability of certain functional equations via a fixed point of Ciric

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 121-127 ◽  
Author(s):  
Mohamed Akkouchi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
The Stability

Let S be a non empty set. We prove the stability (in the sense of Ulam) of the functional equation: f(t)=F(t,f (?(t))), where ? is a given function of S into itself and F is a function satisfying a contraction of Ciric type ([5]). Our analysis is based on the use of a fixed point theorem of Ciric (see [5] and [4]). In particular our result provides a generalization and a natural continuation of a paper of Baker (see [3]).

scholarly journals Orthogonal stability of the generalized quadratic functional equations in the sense of Rätz

2019 ◽  
Vol 52 (1) ◽  
pp. 523-530
Author(s):  
Laddawan Aiemsomboon ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Algebra ◽  
Point Theorem ◽  
Functional Equations ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Banach Module ◽  
Unital Banach Algebra

AbstractLet (X, ⊥) be an orthogonality module in the sense of Rätz over a unital Banach algebra A and Y be a real Banach module over A. In this paper, we apply the alternative fixed point theorem for proving the Hyers-Ulam stability of the orthogonally generalized k-quadratic functional equation of the formaf(kx + y) + af(kx - y) = f(ax + ay) + f(ax - ay) + \left( {2{k^2} - 2} \right)f(ax)for some |k| > 1, for all a ɛ A1 := {u ɛ A||u|| = 1} and for all x, y ɛ X with x⊥y, where f maps from X to Y.

scholarly journals Nearly Ternary Quadratic Higher Derivations on Non-Archimedean Ternary Banach Algebras: A Fixed Point Approach

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
M. B. Ghaemi ◽  
J. M. Rassias ◽  
Badrkhan Alizadeh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Banach Algebras ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Fixed Point Approach ◽  
Ternary Algebras ◽  
The Stability

We investigate the stability and superstability of ternary quadratic higher derivations in non-Archimedean ternary algebras by using a version of fixed point theorem via quadratic functional equation.

scholarly journals The Stability of a General Sextic Functional Equation by Fixed Point Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jaiok Roh ◽  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Fixed Point Theorem ◽  
The Stability

In this paper, we will consider the generalized sextic functional equation ∑ i = 0 7   7 C i − 1 7 − i f x + i y = 0 . And by applying the fixed point theorem in the sense of C a ˘ dariu and Radu, we will discuss the stability of the solutions for this functional equation.

scholarly journals A New Coupled Fixed Point Result in Extended Metric Spaces with an Application to Study the Stability of Set-Valued Functional Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Ahmed H. Soliman ◽  
A. M. Zidan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Functional Equations ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Generalized Metric Space ◽  
Coupled Fixed Point Theorem ◽  
The Stability

In this paper, we introduce a new coupled fixed point theorem in a generalized metric space and utilize the same to study the stability for a system of set-valued functional equations.

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.

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.

scholarly journals Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammad Esmael Samei ◽  
Ahmad Ahmadi ◽  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
Shahram Rezapour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Schauder Fixed Point Theorem ◽  
Stability Of Solution ◽  
The Stability ◽  
Well Posed ◽  
Schauder Fixed Point ◽  
Schäuder Fixed Point Theorem

AbstractIn this paper, we propose the conditions on which a class of boundary value problems, presented by fractional q-differential equations, is well-posed. First, under the suitable conditions, we will prove the existence and uniqueness of solution by means of the Schauder fixed point theorem. Then, the stability of solution will be discussed under the perturbations of boundary condition, a function existing in the problem, and the fractional order derivative. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

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