scholarly journals Set valued integrability in non separable Fréchet spaces and applications

2016 ◽  
Vol 66 (5) ◽  
Author(s):  
L. Di Piazza ◽  
V. Marraffa ◽  
B. Satco
Keyword(s):  
Fréchet Spaces ◽  
Measurable Multifunctions

AbstractWe focus on measurability and integrability for set valued functions in non-necessarily separable Fréchet spaces. We prove some properties concerning the equivalence between different classes of measurable multifunctions. We also provide useful characterizations of Pettis set-valued integrability in the announced framework. Finally, we indicate applications to Volterra integral inclusions.

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

Fixed point sets for abstract volterra operators on fréchet spaces

2000 ◽  
Vol 76 (1-2) ◽  
pp. 131-152 ◽  
Author(s):  
Dana M. Bedivan ◽  
Donal O′Regan
Keyword(s):  
Fixed Point ◽  
Fréchet Spaces ◽  
Point Sets ◽  
Volterra Operators ◽  
Fixed Point Sets
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