scholarly journals Nearly Radical Quadratic Functional Equations inp-2-Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Khodaei ◽  
A. Ebadian ◽  
G. H. Kim
Keyword(s):  
Functional Equations ◽  
Quadratic Functional ◽  
Normed Spaces

scholarly journals On the probabilistic stability of some functional equations

2013 ◽  
Vol 29 (1) ◽  
pp. 125-132
Author(s):  
CLAUDIA ZAHARIA ◽  
◽  
DOREL MIHET ◽  
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Of Functional Equations ◽  
The Stability ◽  
Stability Results

We establish stability results concerning the additive and quadratic functional equations in complete Menger ϕ-normed spaces by using fixed point theory. As particular cases, some theorems regarding the stability of functional equations in β - normed and quasi-normed spaces are obtained.

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 On the stability problem of quadratic functional equations in 2-Banach spaces

2017 ◽  
pp. 5054-5061
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Stability Problem ◽  
Functional Equations ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability ◽  
Stability Results

In this paper, we investigate the stability problem in the spirit of Hyers-Ulam, Rassias and G·avruta for the quadratic functional equation:f(2x + y) + f(2x ¡ y) = 2f(x + y) + 2f(x ¡ y) + 4f(x) ¡ 2f(y) in 2-Banach spaces. These results extend the generalized Hyers-Ulam stability results by thequadratic functional equation in normed spaces to 2-Banach spaces.

scholarly journals A General System of Euler–Lagrange-Type Quadratic Functional Equations in Menger Probabilistic Non-Archimedean 2-Normed Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
M. B. Ghaemi ◽  
Y. J. Cho ◽  
H. Majani
Keyword(s):  
Functional Equations ◽  
General System ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Rassias Stability

We prove the generalized Hyers-Ulam-Rassias stability of a general system of Euler-Lagrange-type quadratic functional equations in non-Archimedean 2-normed spaces and Menger probabilistic non-Archimedean-normed spaces.

scholarly journals Inner product spaces and quadratic functional equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jae-Hyeong Bae ◽  
Batool Noori ◽  
M. B. Moghimi ◽  
Abbas Najati
Keyword(s):  
Functional Equations ◽  
Quadratic Functions ◽  
Inner Product ◽  
Quadratic Functional ◽  
Product Spaces ◽  
Normed Spaces ◽  
Inner Product Spaces ◽  
Restricted Domains ◽  
The Stability

AbstractIn this paper, we introduce the functional equations $$\begin{aligned} f(2x-y)+f(x+2y)&=5\bigl[f(x)+f(y)\bigr], \\ f(2x-y)+f(x+2y)&=5f(x)+4f(y)+f(-y), \\ f(2x-y)+f(x+2y)&=5f(x)+f(2y)+f(-y), \\ f(2x-y)+f(x+2y)&=4\bigl[f(x)+f(y)\bigr]+\bigl[f(-x)+f(-y)\bigr]. \end{aligned}$$ f ( 2 x − y ) + f ( x + 2 y ) = 5 [ f ( x ) + f ( y ) ] , f ( 2 x − y ) + f ( x + 2 y ) = 5 f ( x ) + 4 f ( y ) + f ( − y ) , f ( 2 x − y ) + f ( x + 2 y ) = 5 f ( x ) + f ( 2 y ) + f ( − y ) , f ( 2 x − y ) + f ( x + 2 y ) = 4 [ f ( x ) + f ( y ) ] + [ f ( − x ) + f ( − y ) ] . We show that these functional equations are quadratic and apply them to characterization of inner product spaces. We also investigate the stability problem on restricted domains. These results are applied to study the asymptotic behaviors of these quadratic functions in complete β-normed spaces.

scholarly journals Random Stability of Quadratic Functional Equations

2019 ◽  
Vol 16 (1) ◽  
pp. 498-507
Author(s):  
Mee Kwang Kang
Keyword(s):  
Functional Equation ◽  
Positive Integer ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Random Normed Spaces ◽  
Fixed Positive Integer

In this paper, we investigate the generalized Hyers-Ulam stability on random -normed spaces associated with the following generalized quadratic functional equation ,where  is a fixed positive integer via two methods

scholarly journals On the stability of the quadratic mapping in normed spaces

2001 ◽  
Vol 25 (4) ◽  
pp. 217-229 ◽  
Author(s):  
Gwang Hui Kim
Keyword(s):  
Functional Equations ◽  
Quadratic Functional ◽  
Quadratic Mapping ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability ◽  
Rassias Stability

The Hyers-Ulam stability, the Hyers-Ulam-Rassias stability, and also the stability in the spirit of Gavruţa for each of the following quadratic functional equationsf(x+y)+f(x−y)=2f(x)+2f(y),f(x+y+z)+f(x−y)+f(y−z)+f(z−x)=3f(x)+3f(y)+3f(z),f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(z+x)are investigated.

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