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Some Result of Stability and Spectra Properties on Semigroup of Linear Operator
Department of Mathematics, University of Ilorin, Ilorin, Nigeria
Department of Mathematics, University of Ilorin, Ilorin, Nigeria
Department of Mathematics, University of Ilorin, Ilorin, Nigeria
Department of Mathematics, University of Ilorin, Ilorin, Nigeria
Department of Mathematics, University of Ilorin, Ilorin, Nigeria
- 1 Department of Mathematics, University of Ilorin, Ilorin, Nigeria
- 2 Department of Mathematics, University of Ilorin, Ilorin, Nigeria
- 3 Department of Mathematics, University of Ilorin, Ilorin, Nigeria
- 4 Department of Mathematics, University of Ilorin, Ilorin, Nigeria
- 5 Department of Mathematics, University of Ilorin, Ilorin, Nigeria
Advances in Pure Mathematics·Volume 09 (2019)·Pages 43–51·Published 10 January 2019·DOI10.4236/apm.2019.91003
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Abstract
This paper consists of some properties of a new subclass of semigroup of linear operator. The stability and spectra analysis of ω -order preserving partial contraction mapping ( ω - OCP n ) are obtained. The results show that operators on the proposed ω - OCP n are densely defined and closed. Several existing results in the literature are contained in this work.
KeywordsContraction MappingSemigroupBanach SpaceResolvent and Bounded Operator
- Banach, S. (1922) Surles Operation Dam Les Eusembles Abstracts et lear Application Aus Equation Integrals. Fundamenta Mathematicae, 3, 133-181. https://doi.org/10.4064/fm-3-1-133-181
- Batty, C.J.K. (1996) Spectral Condition for Stabilty of One-Parameter Semigroup. Journal of Differential Equations, 127, 87-96. https://doi.org/10.1006/jdeq.1996.0062
- Batty, C.J.K., Chill, R. and Tomilov, Y. (2002) Strong Stability of Bounded Evolution Families and Semigroup. Journal of Functional Analysis, 193, 116-139. https://doi.org/10.1006/jfan.2001.3917
- Chill, R. and Tomilov, Y. (2007) Stability Operator Semigroup. Banach Center Publication 75, Polish Academy of Sciences, Warsaw, 71-73.
- Rabiger, F. and Wolf, M.P.H. (2000) Spectral and Asymptotic Properties of Resolvent Dominated-Operators. Journal of the Australian Mathematical Society Series A, 68, 181-201. https://doi.org/10.1017/S1446788700001944
- Ambrozie, C. and Müller, V. (2004) Invariant Subspaces for Polynomially Bounded Operators. Journal of Functional Analysis, 213, 321-345. https://doi.org/10.1016/j.jfa.2003.12.004
- Balakrishnan, A.V. (1960) Fractional Powers of Closed Operators and Semigroups Generated by Them. Pacific Journal of Mathematics, 10, 419-437. https://doi.org/10.2140/pjm.1960.10.419
- Ioan, I.V. (2003) C0-Semigroups and Applications. Mathematics Studies, 191, Elservier, North-Holland.
- Engel, K. and Nagel, R. (1999) One-Parameter Semigroups for Linear Equations. Graduate Texts in Mathematics, 194, Springer, New York.
- Rauf, K. and Akinyele, A.Y. (2019) Properties of ω-Order-Preserving Partial Contraction Mapping and Its Relation to C0-Semigroup. International Journal of Mathematics and Computer Science, 14, 61-68.
- Bellem-Morante, A. and McBride, A. (1998) Applied Non-Linear Semigroups. Mathematics Methods in Practices. John Wiley and Sons, Chichester.
- Brezis, H. (2011) Functional Analysis, Sobolev Space and Partial Differential Equations. Springer, Berlin.