scholarly journals The exactness of the projective limit functor on the category of quotients of Frechet spaces

2008 ◽  
Vol 58 (1) ◽  
pp. 173-181
Author(s):  
Belmesnaoui Aqzzouz
Keyword(s):  
Projective Limit ◽  
Fréchet Spaces

scholarly journals Dual characterization of the Dieudonne-Schwartz theorem on bounded sets

1983 ◽  
Vol 6 (1) ◽  
pp. 189-192 ◽  
Author(s):  
C. Bosch ◽  
J. Kucera ◽  
K. McKennon
Keyword(s):  
Inductive Limit ◽  
Projective Limit ◽  
Fréchet Spaces ◽  
Inductive Limits ◽  
Counter Example ◽  
Bounded Sets ◽  
Strong Dual

The Dieudonné-Schwartz Theorem on bounded sets in a strict inductive limit is investigated for non-strict inductive limits. Its validity is shown to be closely connected with the problem of whether the projective limit of the strong duals is a strong dual itself. A counter-example is given to show that the Dieudonné-Schwartz Theorem is not in general valid for an inductive limit of a sequence of reflexive, Fréchet spaces.

scholarly journals On the domain of implicit functions in a projective limit setting without additional norm estimates

2020 ◽  
Vol 53 (1) ◽  
pp. 112-120 ◽  
Author(s):  
Jean-Pierre Magnot
Keyword(s):  
Inverse Function ◽  
Projective Limit ◽  
Inverse Function Theorem ◽  
Open Ball ◽  
Fréchet Spaces ◽  
Implicit Functions ◽  
Frobenius Theorem ◽  
Norm Estimates ◽  
Limit Setting ◽  
Open Question

AbstractWe examine how implicit functions on ILB-Fréchet spaces can be obtained without metric or norm estimates which are classically assumed. We obtain implicit functions defined on a domain D which is not necessarily open, but which contains the unit open ball of a Banach space. The corresponding inverse function theorem is obtained, and we finish with an open question on the adequate (generalized) notion of differentiation, needed for the corresponding version of the Fröbenius theorem.

scholarly journals Fixed points of cone compression and expansion multimaps defined on Fréchet spaces: The projective limit approach

2006 ◽  
Vol 2006 ◽  
pp. 1-13 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Projective Limit ◽  
Fréchet Space ◽  
Frechet Space ◽  
Fréchet Spaces ◽  
Multivalued Maps ◽  
Compression And Expansion

We present a generalization of the cone compression and expansion results due to Krasnoselskii and Petryshyn for multivalued maps defined on a Fréchet space E. The proof relies on fixed point results in Banach spaces and viewing E as the projective limit of a sequence of Banach spaces.

scholarly journals Fixed point theory for Mönch-type maps defined on closed subsets of Fréchet spaces: the projective limit approach

2005 ◽  
Vol 2005 (17) ◽  
pp. 2775-2782 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Jewgeni H. Dshalalow ◽  
Donal O'Regan
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Projective Limit ◽  
Fréchet Space ◽  
Frechet Space ◽  
Fréchet Spaces

New Leray-Schauder alternatives are presented for Mönch-type maps defined between Fréchet spaces. The proof relies on viewing a Fréchet space as the projective limit of a sequence of Banach spaces.

Representations of the spaces Cm(Ω) ∩ Hk, p (Ω)

1996 ◽  
Vol 120 (3) ◽  
pp. 489-498 ◽  
Author(s):  
A. A. Albanese ◽  
G. Metafune ◽  
V. B. Moscatelli
Keyword(s):  
Banach Spaces ◽  
Function Space ◽  
Inductive Limit ◽  
Projective Limit ◽  
Fréchet Space ◽  
Frechet Space ◽  
Fréchet Spaces ◽  
Complemented Subspaces ◽  
Complemented Subspace ◽  
Strong Dual

The present work has its motivation in the papers [2] and [6] on distinguished Fréchet function spaces. Recall that a Fréchet space E is distinguished if it is the projective limit of a sequence of Banach spaces En such that the strong dual E′β is the inductive limit of the sequence of the duals E′n. Clearly, the property of being distinguished is inherited by complemented subspaces and in [6] Taskinen proved that the Fréchet function space C(R) ∩ L1(R) (intersection topology) is not distinguished, by showing that it contains a complemented subspace of Moscatelli type (see Section 1) that is not distinguished. Because of the criterion in [1], it is easy to decide when a Frechet space of Moscatelli type is distinguished. Using this, in [2], Bonet and Taskinen obtained that the spaces open in RN) are distinguished, by proving that they are isomorphic to complemented subspaces of distinguished Fréchet spaces of Moscatelli type.

Measure of noncompactness and semilinear differential equations in Fréchet spaces

2019 ◽  
Vol 12 (1) ◽  
pp. 69-81 ◽  
Author(s):  
Amaria Arara ◽  
Mouffak Benchohra ◽  
Fatima Mesri
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Fréchet Spaces

scholarly journals Common Fixed Point and Invariant Approximation Results on Non-Starshaped Domains

2005 ◽  
Vol 12 (4) ◽  
pp. 659-669
Author(s):  
Nawab Hussain ◽  
Donal O'Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fréchet Spaces ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Invariant Approximation ◽  
Commuting Maps

Abstract We extend the concept of 𝑅-subweakly commuting maps due to Shahzad [J. Math. Anal. Appl. 257: 39–45, 2001] to the case of non-starshaped domains and obtain common fixed point results for this class of maps on non-starshaped domains in the setup of Fréchet spaces. As applications, we establish Brosowski–Meinardus type approximation theorems. Our results unify and extend the results of Al-Thagafi, Dotson, Habiniak, Jungck and Sessa, Sahab, Khan and Sessa and Shahzad.

scholarly journals Existence results for some integro-differential equations with state-dependent nonlocal conditions in Fréchet Spaces

2020 ◽  
Vol 7 (1) ◽  
pp. 272-280
Author(s):  
Mamadou Abdoul Diop ◽  
Kora Hafiz Bete ◽  
Reine Kakpo ◽  
Carlos Ogouyandjou
Keyword(s):  
Differential Equations ◽  
Resolvent Operator ◽  
Mild Solutions ◽  
Linear Part ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Fréchet Spaces ◽  
Local Conditions ◽  
State Dependent ◽  
Darbo Fixed Point Theorem

AbstractIn this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer. The existence of mild solutions is proved by means of Kuratowski’s measure of non-compactness and a generalized Darbo fixed point theorem in Fréchet space. Finally, an example is given for demonstration.

scholarly journals Fréchet Spaces via Fuzzy Structures

2021 ◽  
Vol 1818 (1) ◽  
pp. 012082
Author(s):  
Ahmad Ghanawi Jasim ◽  
Z. D. Al-Nafie
Keyword(s):  
Fréchet Spaces
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