TITLE:
Boundedness Types of Perturbations on the Growth of Semigroups
AUTHORS:
Zuheir Khidir Ahmed Abdelgader, Nariman Khider Ahmed Abdalgadir, Entisar Bakhit Bashir Elshikh, Abualez Alamin Ahmed Ali
KEYWORDS:
Cesáro Average, C0-Semigroups, Boundedness, Perturbation Stability, Hille-Yosida, Growth of Sequences
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.13 No.1,
January
19,
2023
ABSTRACT: We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕj-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.