Abstract
The aim of this work is to introduce the domain and the
Favard spaces of order $\alpha$ where $\alpha\in]0,1]$ for
$k$-regularized resolvent family, extending some of the
well-known theorems for semigroup and resolvent
family. Furthermore, we show some relationship between the
Favard temporal spaces and the Favard frequential spaces
for scalar Volterra linear systems in Banach spaces,
extending some results in [8,3].
Метою цієї роботи є ввести область та простори
Фавара порядку $ \alpha$, де $ \alpha \in] 0,1] $ для $k $
-- регуляризованої сім'ї резольвент, та розширити деякі з
добре відомих теорем для напівгруп і сімей
резольвент. Крім того, ми показуємо деякий взаємозв'язок
між часовими просторами Фавара та просторовими просторами
Фавара для скалярних лінійних систем Вольтерра в банахових
просторах, розширюючи деякі результати в [8,3].
Key words: Semigroups, Volterra integral equations, regularized resolvent families, Favard spaes.
Full Text
Article Information
| Title | Regularized solutions for abstract Volterra equations |
| Source | Methods Funct. Anal. Topology, Vol. 28 (2022), no. 4, 309-323 |
| DOI | 10.31392/MFAT-npu26_4.2022.04 |
| MathSciNet |
MR4685366 |
| Milestones | Reeived 18/10/2022; Revised 25/10/2022 |
| Copyright | The Author(s) 2022 (CC BY-SA) |
Authors Information
Fouad Maragh
Laboratory LMA, Department of Mathematis, Faulty of sienes, Ibn Zohr University, PB 80000 Agadir, Moroo.
Ahmed Fadili
Laboratory LIMATI, Department of Mathematis and Informatis, Polydisiplinary Faulty, Sultan Moulay Slimane University, Mghila, PB 592 Beni Mellal, Moroo.
Citation Example
Fouad Maragh and Ahmed Fadili, Regularized solutions for abstract Volterra equations, Methods Funct. Anal. Topology 28
(2022), no. 4, 309-323.
BibTex
@article {MFAT1884,
AUTHOR = {Fouad Maragh and Ahmed Fadili},
TITLE = {Regularized solutions for abstract Volterra equations},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {28},
YEAR = {2022},
NUMBER = {4},
PAGES = {309-323},
ISSN = {1029-3531},
MRNUMBER = {MR4685366},
DOI = {10.31392/MFAT-npu26_4.2022.04},
URL = {http://mfat.imath.kiev.ua/article/?id=1884},
}
