scholarly journals On the stability of a quadratic functional equation over non-Archimedean spaces

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2693-2704
Author(s):  
Gastão Bettencourt ◽  
Sérgio Mendes
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Abelian Group ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
The Stability ◽  
Rassias Stability

Let G be an abelian group and suppose that X is a non-Archimedean Banach space. We study Hyers-Ulam-Rassias stability for the functional equation of quadratic type f(x+y+z)+ f(x)+f(y)+f(z)=f(x+y)+f(y+z)+ f(z+x) where f : G ? X is a map.

scholarly journals On the Stability of Quadratic Functional Equations inF-Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Xiuzhong Yang
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
The Stability ◽  
Rassias Stability

The Hyers-Ulam-Rassias stability of quadratic functional equationf(2x+y)+f(2x-y)=f(x+y)+f(x-y)+6f(x)and orthogonal stability of the Pexiderized quadratic functional equationf(x+y)+f(x-y)=2g(x)+2h(y)inF-spaces are proved.

On the Hyers–Ulam stability and hyperstability of a generalized quadratic functional equation in n-Banach spaces

2021 ◽  
pp. 2250013
Author(s):  
Nordine Bounader
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Abelian Group ◽  
Banach Spaces ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Class Of Functions

In this paper, we establish some Hyers–Ulam stability and hyperstability results of the following functional equation [Formula: see text] in the class of functions from an abelian group [Formula: see text] into a [Formula: see text]-Banach space.

Stability of Generalized Quadratic Functional Equation in Non-Archimedean Fuzzy Normed Spaces

2011 ◽  
Vol 403-408 ◽  
pp. 879-887
Author(s):  
K. Ravi ◽  
P. Narasimman
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Rassias Stability

In this paper, we obtain the general solution and investigate the Hyers-Ulam-Rassias stability of the Generalized Quadratic functional equation in non-Archimedean fuzzy 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.

Sign in / Sign up

Export Citation Format

Share Document