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 Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN spaces

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3063
Author(s):  
Kandhasamy Tamilvanan ◽  
Abdulaziz Mohammed Alanazi ◽  
John Michael Rassias ◽  
Ali H. Alkhaldi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Quadratic Mapping ◽  
Normed Spaces ◽  
Intuitionistic Fuzzy ◽  
Fixed Point Techniques ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Stability Results

In this paper, we use direct and fixed-point techniques to examine the generalised Ulam–Hyers stability results of the general Euler–Lagrange quadratic mapping in non-Archimedean IFN spaces (briefly, non-Archimedean Intuitionistic Fuzzy Normed spaces) over a field.

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.

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.

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.

Stability of Quadratic Functional Equation in Fuzzy Banach Space

2013 ◽  
Vol 373-375 ◽  
pp. 1881-1884
Author(s):  
Xiao Jing Zhan ◽  
Pei Sheng Ji
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fuzzy Banach Space

In this paper, we investigate the Hyers-Ulam stability of the functional equation ƒ(2x+y)+ƒ(2x-y)=8ƒ(x)+2ƒ(y) in fuzzy Banach space using the fixed point method.

scholarly journals A New Approach to Hyers-Ulam Stability of r -Variable Quadratic Functional Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Vediyappan Govindan ◽  
Porpattama Hammachukiattikul ◽  
Grienggrai Rajchakit ◽  
Nallappan Gunasekaran ◽  
R. Vadivel
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Quadratic Mapping ◽  
Ulam Stability ◽  
New Approach

In this paper, we investigate the general solution of a new quadratic functional equation of the form ∑ 1 ≤ i < j < k ≤ r ϕ l i + l j + l k = r − 2 ∑ i = 1 , i ≠ j r ϕ l i + l j + − r 2 + 3 r − 2 / 2 ∑ i = 1 r ϕ l i . We prove that a function admits, in appropriate conditions, a unique quadratic mapping satisfying the corresponding functional equation. Finally, we discuss the Ulam stability of that functional equation by using the directed method and fixed-point method, respectively.

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