On the stability of the linear mapping in Banach spaces

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.

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Superstability of adjointable mappings on Hilbert c∗-modules

Applicable Analysis and Discrete Mathematics ◽

10.2298/aadm0901039f ◽

2009 ◽

Vol 3 (1) ◽

pp. 39-45 ◽

Cited By ~ 1

Author(s):

M. Frank ◽

P. Găvruţa ◽

M.S. Moslehian

Keyword(s):

Banach Spaces ◽

Linear Mapping ◽

Stability Theorem ◽

Classical Sense ◽

C Algebra ◽

The Stability ◽

Densely Defined ◽

Rassias Stability

We define the notion of ?-perturbation of a densely defined adjointable mapping and prove that any such mapping f between Hilbert A-modules over a fixed C*-algebra A with densely defined corresponding mapping g is A-linear and adjointable in the classical sense with adjoint g. If both f and g are every- where defined then they are bounded. Our work concerns with the concept of Hyers-Ulam-Rassias stability originated from the 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]. We also indicate complementary results in the case where the Hilbert C?-modules admit non-adjointable C*-linear mappings.

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Numerical Reckoning Fixed Points of (ρE)-Type Mappings in Modular Vector Spaces

Mathematics ◽

10.3390/math7050390 ◽

2019 ◽

Vol 7 (5) ◽

pp. 390 ◽

Cited By ~ 3

Author(s):

Wissam Kassab ◽

Teodor Ţurcanu

Keyword(s):

Fixed Points ◽

Banach Spaces ◽

Iteration Process ◽

Existence Results ◽

Data Dependence ◽

Vector Spaces ◽

The Stability ◽

Recent Version

In this paper, we study an iteration process introduced by Thakur et al. for Suzuki mappings in Banach spaces, in the new context of modular vector spaces. We establish existence results for a more recent version of Suzuki generalized non-expansive mappings. The stability and data dependence of the scheme for ρ -contractions is studied as well.

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ON THE STABILITY OF THE DIFFERENTIAL PROCESS GENERATED BY COMPLEX INTERPOLATION

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s1474748020000080 ◽

2020 ◽

pp. 1-32

Author(s):

Jesús M. F. Castillo ◽

Willian H. G. Corrêa ◽

Valentin Ferenczi ◽

Manuel González

Keyword(s):

Unit Circle ◽

Banach Spaces ◽

Local Stability ◽

Interpolation Method ◽

Complex Interpolation ◽

Analytic Family ◽

Köthe Spaces ◽

The Stability ◽

Stability Results ◽

Differential Process

We study the stability of the differential process of Rochberg and Weiss associated with an analytic family of Banach spaces obtained using the complex interpolation method for families. In the context of Köthe function spaces, we complete earlier results of Kalton (who showed that there is global bounded stability for pairs of Köthe spaces) by showing that there is global (bounded) stability for families of up to three Köthe spaces distributed in arcs on the unit circle while there is no (bounded) stability for families of four or more Köthe spaces. In the context of arbitrary pairs of Banach spaces, we present some local stability results and some global isometric stability results.

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Simple eigenvalues and bifurcation for a multiparameter problem

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500006593 ◽

1988 ◽

Vol 31 (1) ◽

pp. 77-88 ◽

Cited By ~ 3

Author(s):

D. F. McGhee ◽

M. H. Sallam

Keyword(s):

Banach Spaces ◽

Simple Eigenvalue ◽

Linear Mapping ◽

Spectral Parameters ◽

Non Linear ◽

Multiparameter Problem ◽

Image Position ◽

Bifurcation Of Solutions

We are concerned with the problem of bifurcation of solutions of a non-linear multiparameter problem at a simple eigenvalue of the linearised problem.Let X and Y be real Banach spaces, and let A, Bi, i = 1, …, n∈B(X, Y). Let : Rn × X → Y be a non-linear mapping. We consider the equationwhereand λ=(λ1, λ2,…,λn) ∈ Rn is an n-tuple of spectral parameters.

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On the stability of radical septic functional equations

Mathematics ◽

10.3390/math8122229 ◽

2020 ◽

Vol 8 (12) ◽

pp. 2229

Author(s):

Emanuel Guariglia ◽

Kandhasamy Tamilvanan

Keyword(s):

Functional Equation ◽

Approximate Solution ◽

Vector Space ◽

Banach Spaces ◽

Functional Equations ◽

Normed Vector Space ◽

Relevant Case ◽

The Stability ◽

Normed Vector ◽

Stability Results

This paper deals with the approximate solution of the following functional equation fx7+y77=f(x)+f(y), where f is a mapping from R into a normed vector space. We show stability results of this equation in quasi-β-Banach spaces and (β,p)-Banach spaces. We also prove the nonstability of the previous functional equation in a relevant case.

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