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 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.

scholarly journals A New Fixed Point Theorem and a New Generalized Hyers-Ulam-Rassias Stability in Incomplete Normed Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1117
Author(s):  
Maryam Ramezani ◽  
Ozgur Ege ◽  
Manuel De la Sen
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Rassias Stability

In this study, our goal is to apply a new fixed point method to prove the Hyers-Ulam-Rassias stability of a quadratic functional equation in normed spaces which are not necessarily Banach spaces. The results of the present paper improve and extend some previous results.

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

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