A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

scholarly journals A Fixed Point Approach to the Stability of ann-Dimensional Mixed-Type Additive and Quadratic Functional Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Mixed Type ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Stability Problems ◽  
Fixed Point Approach ◽  
The Stability

We investigate the stability problems for a functional equation2f(∑j=1nxj)+∑1≤i,j≤n,  i≠jf(xi-xj)=(n+1)∑j=1nf(xj)+(n-1)∑j=1nf(-xj)by using the fixed point method.

scholarly journals Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

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 A Fixed Point Approach to the Stability of a Cauchy-Jensen Functional Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Jae-Hyeong Bae ◽  
Won-Gil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Fixed Point Approach ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
The Stability

We find out the general solution of a generalized Cauchy-Jensen functional equation and prove its stability. In fact, we investigate the existence of a Cauchy-Jensen mapping related to the generalized Cauchy-Jensen functional equation and prove its uniqueness. In the last section of this paper, we treat a fixed point approach to the stability of the Cauchy-Jensen functional equation.

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.

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