scholarly journals Hyers–Ulam–Rassias Stability of Additive Mappings in Fuzzy Normed Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Jianrong Wu ◽  
Lingxiao Lu
Keyword(s):  
Functional Equations ◽  
Normed Spaces ◽  
Additive Mappings ◽  
Rassias Stability

In this paper, the Hyers–Ulam–Rassias stabilities of two functional equations, f a x + b y = r f x + s f y and f x + y + z = 2 f x + y / 2 + f z , are investigated in the framework of fuzzy normed 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 Direct Method and Approximation of the Reciprocal Difference Functional Equations in Various Normed Spaces

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
H. Azadi Kenary
Keyword(s):  
Functional Equations ◽  
Direct Method ◽  
Normed Spaces ◽  
Reciprocal Difference ◽  
Rassias Stability

AbstractIn this paper, using direct method, we prove the generalized Hyers- Ulam-Rassias stability of the reciprocal difference functional equations in various normed spaces.

scholarly journals On new stability results for composite functional equations in quasi-β-normed spaces

2021 ◽  
Vol 54 (1) ◽  
pp. 68-84
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Functional Equations ◽  
Direct Method ◽  
Functional Inequality ◽  
Fixed Point Method ◽  
Normed Spaces ◽  
Composite Functional Equations ◽  
Stability Results ◽  
Rassias Stability

Abstract In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f ( f ( x ) − f ( y ) ) = f ( x + y ) + f ( x − y ) − f ( x ) − f ( y ) , f(f\left(x)-f(y))=f\left(x+y)+f\left(x-y)-f\left(x)-f(y), where f f maps from a ( β , p ) \left(\beta ,p) -Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite s s -functional inequality is discussed via our results.

scholarly journals Hyers-Ulam-Rassias RNS Approximation of Euler-Lagrange-Type Additive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
H. Azadi Kenary ◽  
H. Rezaei ◽  
A. Ebadian ◽  
A. R. Zohdi
Keyword(s):  
Functional Equation ◽  
Normed Spaces ◽  
Banach Modules ◽  
Random Normed Spaces ◽  
Additive Mappings ◽  
Rassias Stability

Recently the generalized Hyers-Ulam (or Hyers-Ulam-Rassias) stability of the following functional equation∑j=1mf(-rjxj+∑1≤i≤m,i≠jrixi)+2∑i=1mrif(xi)=mf(∑i=1mrixi)wherer1,…,rm∈R, proved in Banach modules over a unitalC*-algebra. It was shown that if∑i=1mri≠0,ri,rj≠0for some1≤i<j≤mand a mappingf:X→Ysatisfies the above mentioned functional equation then the mappingf:X→Yis Cauchy additive. In this paper we prove the Hyers-Ulam-Rassias stability of the above mentioned functional equation in random normed spaces (briefly RNS).

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.

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.

scholarly journals Solutions and the Generalized Hyers-Ulam-Rassias Stability of a Generalized Quadratic-Additive Functional Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Janfada ◽  
R. Shourvazi
Keyword(s):  
Functional Equation ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
General Solutions ◽  
Rassias Stability

We study general solutions and generalized Hyers-Ulam-Rassias stability of the following -dimensional functional equation , , on non-Archimedean normed spaces.

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