scholarly journals STABILITY OF MAPPINGS ON MULTI-NORMED SPACES

2007 ◽  
Vol 49 (2) ◽  
pp. 321-332 ◽  
Author(s):  
H. G. DALES ◽  
MOHAMMAD SAL MOSLEHIAN
Keyword(s):  
Stability Theorem ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Additive Equation ◽  
Stability Of Mappings ◽  
Rassias Stability

AbstractIn this paper, we define multi-normed spaces, and investigate some properties of multi-bounded mappings on multi-normed spaces. Moreover, we prove a generalized Hyers–Ulam–Rassias stability theorem associated to the Cauchy additive equation for mappings from linear spaces into multi-normed spaces.

scholarly journals HUR-approximation of an ELTA functional equation

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4311-4328
Author(s):  
A.R. Sharifi ◽  
Azadi Kenary ◽  
B. Yousefi ◽  
R. Soltani
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Linear Mapping ◽  
Stability Theorem ◽  
Normed Spaces ◽  
The Stability ◽  
Rassias Stability

The main goal of this paper is study of the Hyers-Ulam-Rassias stability (briefly HUR-approximation) of the following Euler-Lagrange type additive(briefly ELTA) functional equation ?nj=1f (1/2 ?1?i?n,i?j rixi- 1/2 rjxj) + ?ni=1 rif(xi)=nf (1/2 ?ni=1 rixi) where r1,..., rn ? R, ?ni=k rk?0, and ri,rj?0 for some 1? i < j ? n, in fuzzy normed spaces. The concept of HUR-approximation originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

scholarly journals Local stability of mappings on multi-normed spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
Batool Noori ◽  
M. B. Moghimi ◽  
Abbas Najati ◽  
J. M. Rassias
Keyword(s):  
Local Stability ◽  
Normed Spaces ◽  
Stability Of Mappings

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.

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 On the Continuity of Orthogonal Sets in the Sense of Operator Orthogonality

2018 ◽  
Vol 11 (3) ◽  
pp. 793-802
Author(s):  
Mahdi Iranmanesh ◽  
M. Saeedi Khojasteh ◽  
M. K. Anwary
Keyword(s):  
Numerical Range ◽  
Alternative Definition ◽  
Normed Spaces ◽  
Operator Approach ◽  
Linear Spaces ◽  
Continuity Properties ◽  
Lower Semi

In this paper, we introduce the operator approach for orthogonality in linear spaces. In particular, we represent the concept of orthogonal vectors using an operator associated with them, in normed spaces. Moreover, we investigate some of continuity properties of this kind of orthogonality. More precisely, we show that the set valued function F(x; y) = {μ : μ ∈ C, p(x − μy, y) = 1} is upper and lower semi continuous, where p(x, y) = sup{pz1,...,zn−2 (x, y) : z1, . . . , zn−2 ∈ X} and pz1,...,zn−2 (x, y) = kPx,z1,...,zn−2,yk−1 where Px,z1,...,zn−2,y denotes the projection parallel to y from X to the subspace generated by {x, z1, . . . , zn−2}. This can be considered as an alternative definition for numerical range in linear spaces.

GEOMETRIC AND FIXED POINT PROPERTIES IN PRODUCTS OF NORMED SPACES

2019 ◽  
Vol 99 (2) ◽  
pp. 262-273 ◽  
Author(s):  
M. VEENA SANGEETHA
Keyword(s):  
Fixed Point ◽  
Dimensional Subspace ◽  
Point Property ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Nonexpansive Maps ◽  
Uniform Rotundity ◽  
Fixed Point Properties ◽  
Weak Fixed Point Property ◽  
Monotone Norm

Given two (real) normed (linear) spaces $X$ and $Y$, let $X\otimes _{1}Y=(X\otimes Y,\Vert \cdot \Vert )$, where $\Vert (x,y)\Vert =\Vert x\Vert +\Vert y\Vert$. It is known that $X\otimes _{1}Y$ is $2$-UR if and only if both $X$ and $Y$ are UR (where we use UR as an abbreviation for uniformly rotund). We prove that if $X$ is $m$-dimensional and $Y$ is $k$-UR, then $X\otimes _{1}Y$ is $(m+k)$-UR. In the other direction, we observe that if $X\otimes _{1}Y$ is $k$-UR, then both $X$ and $Y$ are $(k-1)$-UR. Given a monotone norm $\Vert \cdot \Vert _{E}$ on $\mathbb{R}^{2}$, we let $X\otimes _{E}Y=(X\otimes Y,\Vert \cdot \Vert )$ where $\Vert (x,y)\Vert =\Vert (\Vert x\Vert _{X},\Vert y\Vert _{Y})\Vert _{E}$. It is known that if $X$ is uniformly rotund in every direction, $Y$ has the weak fixed point property for nonexpansive maps (WFPP) and $\Vert \cdot \Vert _{E}$ is strictly monotone, then $X\otimes _{E}Y$ has WFPP. Using the notion of $k$-uniform rotundity relative to every $k$-dimensional subspace we show that this result holds with a weaker condition on $X$.

scholarly journals Stability of Unbounded Differential Equations in Menger k-Normed Spaces: A Fixed Point Technique

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 400 ◽  
Author(s):  
Masoumeh Madadi ◽  
Reza Saadati ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Normed Spaces ◽  
Fixed Point Technique ◽  
Rassias Stability

We attempt to solve differential equations υ ′ ( ν ) = Γ ( ν , υ ( ν ) ) and use the fixed point technique to prove its Hyers–Ulam–Rassias stability in Menger k-normed spaces.

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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