scholarly journals Generalized Hyers-Ulam stability of general cubic functional equation in random normed spaces

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 89-98
Author(s):  
Seong Kim ◽  
John Rassias ◽  
Nawab Hussain ◽  
Yeol Cho

In this paper, we investigate the generalized Hyers-Ulam stability of a general cubic functional equation: f(x+ky)-kf(x+y)+kf(x-y) -f(x-ky)=2k(k2-1)f(y) for fixed k ? Z+ with k ? 2 in random normed spaces.

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2643-2653
Author(s):  
Zhihua Wang ◽  
Chaozhu Hu

Using the direct method and fixed point method, we investigate the Hyers-Ulam stability of the following cubic ?-functional equation f(x+2y) + f(x-2y)- 2f(x+y)-2f(x-y)-12f(x) = ?(4f(x+y/2) + 4f(x-y/2)-f(x+y)-f(x-y)-6f(x)) in matrix non-Archimedean random normed spaces, where ? is a fixed real number with ? ? 2.


2012 ◽  
Vol 2012 ◽  
pp. 1-45 ◽  
Author(s):  
Yeol Je Cho ◽  
Shin Min Kang ◽  
Reza Saadati

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.


2011 ◽  
Vol 04 (03) ◽  
pp. 413-425 ◽  
Author(s):  
G. Z. Eskandani ◽  
J. M. Rassias ◽  
P. Gavruta

In this paper, we investigate the generalized Hyers-Ulam stability of the following general cubic functional equation [Formula: see text] (k ∈ ℕ, k ≠ 1) in quasi-β-normed spaces and by a counterexample, we will show that this functional equation in a special condition is not stabile.


Filomat ◽  
2011 ◽  
Vol 25 (3) ◽  
pp. 43-54 ◽  
Author(s):  
Eshaghi Gordji ◽  
Bavand Savadkouhi

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).


Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1629-1640 ◽  
Author(s):  
Abasalt Bodaghi

In this paper we obtain the general solution of a mixed additive and quartic functional equation. We also prove the Hyers-Ulam stability of this functional equation in random normed spaces.


2021 ◽  
Vol 6 (1) ◽  
pp. 908-924 ◽  
Author(s):  
Kandhasamy Tamilvanan ◽  
◽  
Jung Rye Lee ◽  
Choonkil Park ◽  
◽  
...  

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