Cauchy–Rassias Stability of Cauchy–Jensen Additive Mappings in Banach Spaces

2006 ◽  
Vol 22 (6) ◽  
pp. 1789-1796 ◽  
Author(s):  
Choonkil Baak
Keyword(s):  
Banach Spaces ◽  
Additive Mappings ◽  
Rassias Stability

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

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 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.

ON APPROXIMATELY ADDITIVE MAPPINGS IN 2-BANACH SPACES

2019 ◽  
Vol 101 (2) ◽  
pp. 299-310 ◽  
Author(s):  
JANUSZ BRZDĘK ◽  
EL-SAYED EL-HADY
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Stability Result ◽  
Main Tool ◽  
Ulam Stability ◽  
Cauchy Equation ◽  
Stability Issues ◽  
Additive Mappings

We show how some Ulam stability issues can be approached for functions taking values in 2-Banach spaces. We use the example of the well-known Cauchy equation $f(x+y)=f(x)+f(y)$, but we believe that this method can be applied for many other equations. In particular we provide an extension of an earlier stability result that has been motivated by a problem of Th. M. Rassias. The main tool is a recent fixed point theorem in some spaces of functions with values in 2-Banach spaces.

scholarly journals On the Stability of Quadratic Functional Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Jung Rye Lee ◽  
Jong Su An ◽  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Positive Integer ◽  
Banach Spaces ◽  
Functional Equations ◽  
Vector Spaces ◽  
Quadratic Functional ◽  
The Stability ◽  
Fixed Positive Integer ◽  
Rassias Stability

LetX,Ybe vector spaces andka fixed positive integer. It is shown that a mappingf(kx+y)+f(kx-y)=2k2f(x)+2f(y)for allx,y∈Xif and only if the mappingf:X→Ysatisfiesf(x+y)+f(x-y)=2f(x)+2f(y)for allx,y∈X. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven.

scholarly journals Approximate multi-Jensen and multi-quadratic mappings in 2-Banach spaces

2013 ◽  
Vol 29 (2) ◽  
pp. 159-166
Author(s):  
KRZYSZTOF CIEPLINSKI ◽  
◽  
TIAN ZHOU XU ◽  
Keyword(s):  
Banach Spaces ◽  
Ulam Stability ◽  
Quadratic Mappings ◽  
Additive Mappings

In this paper we prove the generalized Hyers-Ulam stability of multi-Jensen and multi-quadratic mappings in 2-Banach spaces. The corollaries from our main results correct some outcomes from [Park, W.-G., Approximate additive mappings in 2-Banach spaces and related topics, J. Math. Anal. Appl., 376 (2011) 193–202].

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