scholarly journals On the Hyers-Ulam-Rassias Stability of a General Quintic Functional Equation and a General Sextic Functional Equation

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 510 ◽  
Author(s):  
Yang-Hi Lee
Keyword(s):  
Functional Equation ◽  
Additive Function ◽  
Functional Equations ◽  
Quadratic Function ◽  
Rassias Stability

The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation. In this paper, we investigate Hyers–Ulam–Rassias stability of the general quintic functional equation and the general sextic functional equation.

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 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.

On the generalized orthogonal stability of the pexiderized quadratic functional equations in modular spaces

2017 ◽  
Vol 67 (1) ◽  
Author(s):  
Iz-iddine EL-Fassi ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Modular Spaces ◽  
Generalized Orthogonal ◽  
Rassias Stability

AbstractIn this paper, we establish the Hyers-Ulam-Rassias stability of the quadratic functional equation of Pexiderized type

scholarly journals On the Stability of Quadratic Functional Equations inF-Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Xiuzhong Yang
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
The Stability ◽  
Rassias Stability

The Hyers-Ulam-Rassias stability of quadratic functional equationf(2x+y)+f(2x-y)=f(x+y)+f(x-y)+6f(x)and orthogonal stability of the Pexiderized quadratic functional equationf(x+y)+f(x-y)=2g(x)+2h(y)inF-spaces are proved.

scholarly journals Mixed Type Of Additive And Quintic Functional Equations

2015 ◽  
Vol 29 (1) ◽  
pp. 35-50 ◽  
Author(s):  
Abasalt Bodaghi ◽  
Pasupathi Narasimman ◽  
Krishnan Ravi ◽  
Behrouz Shojaee
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Real Numbers ◽  
Rassias Stability

AbstractIn this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the form $$f\left( {3x + y} \right) - 5f\left( {2x + y} \right) + f\left( {2x - y} \right) + 10f\left( {x + y} \right) - 5f\left( {x - y} \right) = 10f\left( y \right) + 4f\left( {2x} \right) - 8f\left( x \right)$$ in the set of real numbers.

scholarly journals Fuzzy Stability of Quadratic Functional Equations in General Cases

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Ehsan Movahednia
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Rassias Stability

The aim of this paper is to investigate fuzzy Hyers-Ulam-Rassias stability of the general case of quadratic functional equation where and fixed integers with . These functional equations are equivalent. This has been proven by Ulam, 1964.

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).

A Fixed Point Approach to the Stability of Quadratic Functional Equations in Modular Spaces

2017 ◽  
Vol 6 (1) ◽  
pp. 171-175
Author(s):  
Seong Sik Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Fixed Point Approach ◽  
Modular Spaces ◽  
The Stability ◽  
Positive Integers ◽  
Rassias Stability

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equation f(kx + y) + f(kx – y) = 2k2f(x) + 2f(y) for any fixed positive integers k ∈ Ζ+ in modular spaces by using fixed point method.

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.

scholarly journals On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Paisan Nakmahachalasint
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Mixed Type ◽  
General Solutions ◽  
Rassias Stability

In this paper, the mixed-type linear and Euler-Lagrange-Rassias functional equations introduced by J. M. Rassias is generalized to the followingn-dimensional functional equation:f(∑i=1nxi)+(n−2)∑i=1nf(xi)=∑1≤i<j≤nf(xi−xj)whenn>2. We prove the general solutions and investigate its generalized Ulam-Gavruta-Rassias stability.

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