scholarly journals On the lifting of bounded sets in Fréchet spaces

1993 ◽  
Vol 36 (2) ◽  
pp. 277-281 ◽  
Author(s):  
José Bonet ◽  
Susanne Dierolf
Keyword(s):  
Topological Isomorphism ◽  
Fréchet Spaces ◽  
Bounded Sets

This paper considers the behaviour of a quotient map between Fréchet spaces concerning the lifting of bounded sets. The main result shows that a quotient map between Fréchet spaces that lifts bounded sets with closure (or equivalently such that its strong transpose is a topological isomorphism) must also lift bounded sets without closure.

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 Quasi-bounded sets

1990 ◽  
Vol 13 (3) ◽  
pp. 607-610
Author(s):  
Jan Kucera
Keyword(s):  
Fréchet Space ◽  
Locally Convex Spaces ◽  
Frechet Space ◽  
Fréchet Spaces ◽  
Bounded Set ◽  
Bounded Sets ◽  
Locally Convex ◽  
Convex Spaces

It is proved in [1] & [2] that a set bounded in an inductivelimit E=indlim Enof Fréchet spaces is also bounded in someEniffEis fast complete. In the case of arbitrary locally convex spacesEnevery bounded set in a fast completeindlim Enis quasi-bounded in someEn, though it may not be bounded or even contained in anyEn. Every bounded set is quasi-bounded. In a Fréchet space every quasi-bounded set is also bounded.

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

On quotients of non-Archimedean Fréchet spaces

2008 ◽  
Vol 281 (1) ◽  
pp. 147-154 ◽  
Author(s):  
Wiesław Śliwa
Keyword(s):  
Fréchet Spaces

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Type Integral ◽  
Type Spaces ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

Trace inequalities for fractional integrals in mixed norm grand lebesgue spaces

2020 ◽  
Vol 23 (5) ◽  
pp. 1452-1471
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Riesz Potential ◽  
Fractional Integrals ◽  
Mixed Norm ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Grand Lebesgue Spaces ◽  
Measure Spaces ◽  
Necessary And Sufficient ◽  
Bounded Sets ◽  
Trace Inequalities

Abstract D. Adams type trace inequalities for multiple fractional integral operators in grand Lebesgue spaces with mixed norms are established. Operators under consideration contain multiple fractional integrals defined on the product of quasi-metric measure spaces, and one-sided multiple potentials. In the case when we deal with operators defined on bounded sets, the established conditions are simultaneously necessary and sufficient for appropriate trace inequalities. The derived results are new even for multiple Riesz potential operators defined on the product of Euclidean spaces.

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