scholarly journals Probabilistic (Quasi)metric Versions for a Stability Result of Baker

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Dorel Miheţ ◽  
Claudia Zaharia
Keyword(s):  
Functional Equation ◽  
Stability Result ◽  
Fixed Point Method ◽  
Normed Spaces ◽  
Cauchy Functional Equation ◽  
Triangular Norms ◽  
Random Normed Spaces ◽  
The Stability ◽  
Probabilistic Metric ◽  
Additive Cauchy Functional Equation

By using the fixed point method, we obtain a version of a stability result of Baker in probabilistic metric and quasimetric spaces under triangular norms of Hadžić type. As an application, we prove a theorem regarding the stability of the additive Cauchy functional equation in 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 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 On the Stability of an -Variables Functional Equation in Random Normed Spaces via Fixed Point Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. Ebadian ◽  
M. Eshaghi Gordji ◽  
H. Khodaei ◽  
R. Saadati ◽  
Gh. Sadeghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Integer Number ◽  
Normed Spaces ◽  
Random Normed Spaces ◽  
The Stability ◽  
Rassias Stability

At first we find the solution of the functional equation where is an integer number. Then, we obtain the generalized Hyers-Ulam-Rassias stability in random normed spaces via the fixed point method for the above functional equation.

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