The stability of a quadratic functional equation over fuzzy normed spaces of non-Archimedean

2015 ◽  
Author(s):  
Sanfu Wang ◽  
Chun Qi ◽  
Yonghong Shen ◽  
Baoli Xie
Keyword(s):  
Functional Equation ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
The Stability

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 An additive-quadratic functional equation in intuitionistic fuzzy normed spaces

10.26524/cm83 ◽  
2020 ◽  
Vol 4 (2) ◽  
Author(s):  
Soundararajan S ◽  
Suresh Kumar M ◽  
Sudhakar R
Keyword(s):  
Functional Equation ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Intuitionistic Fuzzy ◽  
The Stability ◽  
Intuitionistic Fuzzy Normed Spaces

In this work, we investigate the stability of additive-quadratic (AQ) functional equation in intuitionistic fuzzy normed spaces

scholarly journals Stability of Pexiderized Quadratic Functional Equation in Random 2-Normed Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Mohammed A. Alghamdi
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
The Stability

The aim of this paper is to investigate the stability of Hyers-Ulam-Rassias type theorems by considering the pexiderized quadratic functional equation in the setting of random 2-normed spaces (RTNS), while the concept of random 2-normed space has been recently studied by Goleţ (2005).

APPROXIMATE BIHOMOMORPHISMS AND BIDERIVATIONS IN 3-LIE ALGEBRAS

2012 ◽  
Vol 10 (01) ◽  
pp. 1220020 ◽  
Author(s):  
JAVAD SHOKRI ◽  
ALI EBADIAN ◽  
RASOUL AGHALARI
Keyword(s):  
Functional Equation ◽  
Lie Algebras ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

We prove the generalized Hyers–Ulam stability of mapping on normed spaces for the following 2-dimensional quadratic functional equation: [Formula: see text] Then we apply the results for investigating the stability of bihomomorphisms and biderivations on normed 3-Lie algebras.

scholarly journals Stability of then-Dimensional Mixed-Type Additive and Quadratic Functional Equation in Non-Archimedean Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung ◽  
Themistocles M. Rassias
Keyword(s):  
Functional Equation ◽  
Mixed Type ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
The Stability

We will prove the stability of the functional equation2f(∑i=1nxi)+∑1≤i,j≤n,i≠jf(xi-xj)=(n+1)∑i=1nf(xi)+(n-1)∑i=1nf(-xi)in non-Archimedean normed spaces.

scholarly journals Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Abasalt Bodaghi ◽  
Sang Og Kim
Keyword(s):  
Functional Equation ◽  
Positive Integer ◽  
General Solution ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Additive Functions ◽  
Normed Spaces

We obtain the general solution of the generalized mixed additive and quadratic functional equationfx+my+fx−my=2fx−2m2fy+m2f2y,mis even;fx+y+fx−y−2m2−1fy+m2−1f2y,mis odd, for a positive integerm. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces whenmis an even positive integer orm=3.

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.

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