scholarly journals On the Stability of a General Mixed Additive-Cubic Functional Equation in Random Normed Spaces

2010 ◽  
Vol 2010 (1) ◽  
pp. 328473 ◽  
Author(s):  
TianZhou Xu ◽  
JohnMichael Rassias ◽  
WanXin Xu
Keyword(s):  
Functional Equation ◽  
Normed Spaces ◽  
Cubic Functional Equation ◽  
Random Normed Spaces ◽  
The Stability

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).

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 Nonlinear L-fuzzy stability of k-cubic functional equation

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1137-1148 ◽  
Author(s):  
Reza Saadati ◽  
Yeol Cho ◽  
John Rassias
Keyword(s):  
Functional Equation ◽  
Set Theory ◽  
Normed Space ◽  
Lattice Theory ◽  
Functional Equations ◽  
Stability Result ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Cubic Functional Equation ◽  
The Stability

In this paper, we establish the stability result for the k-cubic functional equation 2[kf (x+ky)+f (kx-y)]=k(k2+1)[f(x+y)+f(x-y)] + 2(k4-1) f(y), where k is a real number different from 0 and 1, in the setting of various L-fuzzy normed spaces that in turn generalize a Hyers-Ulam stability result in the framework of classical normed spaces. First we shall prove the stability of k-cubic functional equations in the L-fuzzy normed space under arbitrary t-norm which generalizes previous works. Then we prove the stability of k-cubic functional equations in the non- Archimedean L-fuzzy normed space. We therefore provide a link among different disciplines: fuzzy set theory, lattice theory, non-Archimedean spaces and mathematical analysis.

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
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Cubic Functional Equation ◽  
Random Normed Spaces

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.

Sign in / Sign up

Export Citation Format

Share Document