scholarly journals A fixed point approach to the stability of a general quartic functional equation

2019 ◽  
Vol 20 (03) ◽  
pp. 207-215 ◽  
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Approach ◽  
Quartic Functional Equation ◽  
The Stability

scholarly journals A Fixed Point Approach to the Stability of a General Mixed AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Tian Zhou Xu ◽  
John Michael Rassias ◽  
Wan Xin Xu
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Fixed Integer ◽  
Fixed Point Approach ◽  
Quartic Functional Equation ◽  
Fixed Point Methods ◽  
The Stability

Using the fixed point methods, we prove the generalized Hyers-Ulam stability of the general mixed additive-quadratic-cubic-quartic functional equationf(x+ky)+f(x−ky)=k2f(x+y)+k2f(x−y)+2(1−k2)f(x)+((k4−k2)/12)[f(2y)+f(−2y)−4f(y)−4f(−y)]for a fixed integerkwithk≠0,±1 in non-Archimedean normed spaces.

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.

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