Author(s)

Zuheir Khidir Ahmed Abdelgader¹, Nariman Khider Ahmed Abdalgadir², Entisar Bakhit Bashir Elshikh¹, Abualez Alamin Ahmed Ali²

¹Department of Mathematics, Faculty of Education, Gezira University, Wad Madani, Sudan.
²Department of Mathematics, Faculty of Education, Holy Quran University, Wad Madani, Sudan.

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 ϕ^j-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.

Cesáro Average, C₀-Semigroups, Boundedness, Perturbation Stability, Hille-Yosida, Growth of Sequences

Abdelgader, Z. , Abdalgadir, N. , Elshikh, E. and Ali, A. (2023) Boundedness Types of Perturbations on the Growth of Semigroups. Advances in Pure Mathematics, 13, 1-10. doi: 10.4236/apm.2023.131001.