On the Aleksandrov problem for mappings preserving fuzzy n-distance in fuzzy n-normed spaces

2019 ◽  
Vol 37 (5) ◽  
pp. 6925-6935
Author(s):  
Hassan Noori Esfahani ◽  
Reza Saadati
Keyword(s):  
Normed Spaces ◽  
Aleksandrov Problem

On the Aleksandrov problem in linear -normed spaces

2004 ◽  
Vol 59 (7) ◽  
pp. 1001-1011 ◽  
Author(s):  
Hahng-Yun Chu ◽  
Keonhee Lee ◽  
Chun-Gil Park
Keyword(s):  
Normed Spaces ◽  
Aleksandrov Problem

Isometry on Linear n-G-quasi Normed Spaces

2017 ◽  
Vol 60 (2) ◽  
pp. 350-363
Author(s):  
Yumei Ma
Keyword(s):  
Normed Space ◽  
Normed Spaces ◽  
Aleksandrov Problem

AbstractThis paper generalizes the Aleksandrov problem: the Mazur-Ulam theoremon n-G-quasi normed spaces. It proves that a one-n-distance preserving mapping is an n-isometry if and only if it has the zero-n-G-quasi preserving property, and two kinds of n-isometries on n-G-quasi normed space are equivalent; we generalize the Benz theorem to n-normed spaces with no restrictions on the dimension of spaces.

scholarly journals The Aleksandrov problem in linear 2-normed spaces

2004 ◽  
Vol 289 (2) ◽  
pp. 666-672 ◽  
Author(s):  
Hahng-Yun Chu ◽  
Chun-Gil Park ◽  
Won-Gil Park
Keyword(s):  
Normed Spaces ◽  
Aleksandrov Problem

On the Aleksandrov problem in linear nn-normed spaces☆

2004 ◽  
Vol 59 (7) ◽  
pp. 1001-1011 ◽  
Author(s):  
H CHU ◽  
K LEE ◽  
C PARK
Keyword(s):  
Normed Spaces ◽  
Aleksandrov Problem

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

scholarly journals Hyers-Ulam stability of quadratic forms in 2-normed spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 496-502
Author(s):  
Won-Gil Park ◽  
Jae-Hyeong Bae
Keyword(s):  
Banach Spaces ◽  
Quadratic Forms ◽  
Functional Equations ◽  
Ulam Stability ◽  
Normed Spaces

AbstractIn this paper, we obtain Hyers-Ulam stability of the functional equationsf (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w),f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w)andf (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w)in 2-Banach spaces. The quadratic forms ax2 + bxy + cy2, ax2 + by2 and axy are solutions of the above functional equations, respectively.

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