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Boundedness Types of Perturbations on the Growth of Semigroups
Department of Mathematics, Faculty of Education, Gezira University, Wad Madani, Sudan
Department of Mathematics, Faculty of Education, Holy Quran University, Wad Madani, Sudan
Department of Mathematics, Faculty of Education, Gezira University, Wad Madani, Sudan
Department of Mathematics, Faculty of Education, Holy Quran University, Wad Madani, Sudan
- 1 Department of Mathematics, Faculty of Education, Gezira University, Wad Madani, Sudan
- 2 Department of Mathematics, Faculty of Education, Holy Quran University, Wad Madani, Sudan
- 3 Department of Mathematics, Faculty of Education, Gezira University, Wad Madani, Sudan
- 4 Department of Mathematics, Faculty of Education, Holy Quran University, Wad Madani, Sudan
Advances in Pure Mathematics·Volume 13 (2023)·Pages 1–10·Published 19 January 2023·DOI10.4236/apm.2023.131001
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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 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.
KeywordsCesáro Average<i>C</i><sub>0</sub>-SemigroupsBoundednessPerturbation StabilityHille-YosidaGrowth of Sequences
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