scholarly journals Solution and Hyers-Ulam-Rassias Stability of Generalized Mixed Type Additive-Quadratic Functional Equations in Fuzzy Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Azadi Kenary ◽  
H. Rezaei ◽  
Y. W. Lee ◽  
G. H. Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Mixed Type ◽  
Direct Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fixed Point Methods ◽  
Rassias Stability

By using fixed point methods and direct method, we establish the generalized Hyers-Ulam stability of the following additive-quadratic functional equationf(x+ky)+f(x−ky)=f(x+y)+f(x−y)+(2(k+1)/k)f(ky)−2(k+1)f(y)for fixed integerskwithk≠0,±1in fuzzy Banach spaces.

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

scholarly journals On the Stability of Quadratic Functional Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Jung Rye Lee ◽  
Jong Su An ◽  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Positive Integer ◽  
Banach Spaces ◽  
Functional Equations ◽  
Vector Spaces ◽  
Quadratic Functional ◽  
The Stability ◽  
Fixed Positive Integer ◽  
Rassias Stability

LetX,Ybe vector spaces andka fixed positive integer. It is shown that a mappingf(kx+y)+f(kx-y)=2k2f(x)+2f(y)for allx,y∈Xif and only if the mappingf:X→Ysatisfiesf(x+y)+f(x-y)=2f(x)+2f(y)for allx,y∈X. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven.

scholarly journals On the stability problem of quadratic functional equations in 2-Banach spaces

2017 ◽  
pp. 5054-5061
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Stability Problem ◽  
Functional Equations ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability ◽  
Stability Results

In this paper, we investigate the stability problem in the spirit of Hyers-Ulam, Rassias and G·avruta for the quadratic functional equation:f(2x + y) + f(2x ¡ y) = 2f(x + y) + 2f(x ¡ y) + 4f(x) ¡ 2f(y) in 2-Banach spaces. These results extend the generalized Hyers-Ulam stability results by thequadratic functional equation in normed spaces to 2-Banach spaces.

scholarly journals A New Fixed Point Theorem and a New Generalized Hyers-Ulam-Rassias Stability in Incomplete Normed Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1117
Author(s):  
Maryam Ramezani ◽  
Ozgur Ege ◽  
Manuel De la Sen
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Rassias Stability

In this study, our goal is to apply a new fixed point method to prove the Hyers-Ulam-Rassias stability of a quadratic functional equation in normed spaces which are not necessarily Banach spaces. The results of the present paper improve and extend some previous results.

scholarly journals Hyers–Ulam Stability of Additive Functional Equation Using Direct and Fixed-Point Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
K. Tamilvanan ◽  
G. Balasubramanian ◽  
Nazek Alessa ◽  
K. Loganathan
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonnegative Integer ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Fixed Point Methods ◽  
Stability Results

In this present work, we obtain the solution of the generalized additive functional equation and also establish Hyers–Ulam stability results by using alternative fixed point for a generalized additive functional equation χ ∑ g = 1 l v g = ∑ 1 ≤ g < h < i ≤ l χ v g + v h + v i − ∑ 1 ≤ g < h ≤ l χ v g + v h − l 2 − 5 l + 2 / 2 ∑ g = 1 l χ v g − χ − v g / 2 . where l is a nonnegative integer with ℕ − 0,1,2,3,4 in Banach spaces.

Solution and stability of an n-dimensional functional equation

Analysis ◽  
2019 ◽  
Vol 39 (3) ◽  
pp. 107-115 ◽  
Author(s):  
Sandra Pinelas ◽  
V. Govindan ◽  
K. Tamilvanan
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
General Solution ◽  
Functional Equations ◽  
Ulam Stability ◽  
Fixed Point Methods ◽  
Fixed Positive Integer

AbstractIn this paper, we prove the general solution and generalized Hyers–Ulam stability of n-dimensional functional equations of the form\sum_{\begin{subarray}{c}i=1\\ i\neq j\neq k\end{subarray}}^{n}f\biggl{(}-x_{i}-x_{j}-x_{k}+\sum_{% \begin{subarray}{c}l=1\\ l\neq i\neq j\neq k\end{subarray}}^{n}x_{l}\biggr{)}=\biggl{(}\frac{n^{3}-9n^{% 2}+20n-12}{6}\biggr{)}\sum_{i=1}^{n}f(x_{i}),where n is a fixed positive integer with \mathbb{N}-\{0,1,2,3,4\}, in a Banach space via direct and fixed point methods.

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 Hyers-Ulam Stability of Quadratic Functional Equation Based on Fixed Point Technique in Banach Spaces and Non-Archimedean Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2575
Author(s):  
Kandhasamy Tamilvanan ◽  
Abdulaziz M. Alanazi ◽  
Maryam Gharamah Alshehri ◽  
Jeevan Kafle
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fixed Point Technique ◽  
Fixed Point Techniques ◽  
Stability Results

In this paper, the authors investigate the Hyers–Ulam stability results of the quadratic functional equation in Banach spaces and non-Archimedean Banach spaces by utilizing two different techniques in terms of direct and fixed point techniques.

scholarly journals The Stability of a Quadratic Functional Equation with the Fixed Point Alternative

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Choonkil Park ◽  
Ji-Hye Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
The Stability

Lee, An and Park introduced the quadratic functional equationf(2x+y)+f(2x−y)=8f(x)+2f(y)and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.

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