The Stability of the Quartic Functional Equation in Random Normed Spaces

2009 ◽  
Vol 110 (2) ◽  
pp. 797-803 ◽  
Author(s):  
D. Miheţ ◽  
R. Saadati ◽  
S. M. Vaezpour
Keyword(s):  
Functional Equation ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
Random Normed Spaces ◽  
The Stability

scholarly journals Nonlinear Random Stability via Fixed-Point Method

2012 ◽  
Vol 2012 ◽  
pp. 1-45 ◽  
Author(s):  
Yeol Je Cho ◽  
Shin Min Kang ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
Random Normed Spaces

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 various complete random normed spaces.

scholarly journals Stability of ann-Dimensional Mixed-Type Additive and Quadratic Functional Equation in Random Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Mixed Type ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Problems ◽  
Random Normed Spaces ◽  
The Stability

We investigate the stability problems for then-dimensional mixed-type additive and quadratic functional equation2f(∑j=1nxj)+∑1≤i,j≤n,  i≠jf(xi-xj)=(n+1)∑j=1nf(xj)+(n-1)∑j=1nf(-xj)in random normed spaces by applying the fixed point method.

scholarly journals On the stability of an AQCQ-functional equation in random normed spaces

2011 ◽  
Vol 2011 (1) ◽  
pp. 34 ◽  
Author(s):  
Choonkil Park ◽  
Sun Young Jang ◽  
Jung Rye Lee ◽  
Dong Yun Shin
Keyword(s):  
Functional Equation ◽  
Normed Spaces ◽  
Random Normed Spaces ◽  
The Stability

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 Stability of a mixed type additive, quadratic and cubic functional equation in random normed spaces

Filomat ◽  
2011 ◽  
Vol 25 (3) ◽  
pp. 43-54 ◽  
Author(s):  
Eshaghi Gordji ◽  
Bavand Savadkouhi
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Mixed Type ◽  
Stability Result ◽  
Normed Spaces ◽  
Cubic Functional Equation ◽  
Random Normed Spaces ◽  
The Stability

In this paper, we obtain the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary t-norms f(x+3y)+f(x?3y)= 9(f(x+y)+f(x?y))?16f(x).

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