This paper consists of dissipative properties and
results of dissipation on infinitesimal generator of a C0-semigroup of ω-order
preserving partial contraction mapping (ω-OCPn) in semigroup of linear
operator. The purpose of this paper is to establish some dissipative properties
on ω-OCPn which have been obtained in the various theorems(research results) and were proved.
References
[1]
Yosida, K. (1948) On the Differentiability and Representation of One-Parameter Semigroups of Linear Operators. Journal of the Mathematical Society of Japan, 1, 15-21. https://doi.org/10.2969/jmsj/00110015
[2]
Miyadera, I. (1952) Generation of Strongly Continuous Semigroups Operators. Tohoku Mathematical Journal, 4, 109-114. https://doi.org/10.2748/tmj/1178245412
[3]
Feller, W. (1953) On the Generation of Unbounded Semigroup of Bounded Linear Operators. Annals of Mathematics, 58, 166-174. https://doi.org/10.2307/1969826
[4]
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
[5]
Lumer, G. and Phillips, R.S. (1961) Dissipative Operators in a Banach Space. Pacific Journal of Mathematics, 11, 679-698. https://doi.org/10.2140/pjm.1961.11.679
[6]
Hille, E. and Phillips, R.S. (1981) Functional Analysis and Semigroups. American Mathematical Society, Providence, Colloquium Publications Vol. 31.
[7]
Batty, C.J.K. (1994) Asymptotic Behaviour of Semigroup of Operators. Banach Center Publications, 30, 35-52. https://doi.org/10.4064/-30-1-35-52
[8]
Engel, K. and Nagel, R. (1999) One-Parameter Semigroup for Linear Evolution Equations. Graduate Texts in Mathematics Vol. 194, Springer, New York.
Laradji, A. and Umar, A. (2004) Combinatorial Results for Semigroups of Order Preserving Partial Transformations. Journal of Algebra, 278, 342-359. https://doi.org/10.1016/j.jalgebra.2003.10.023
[11]
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.
[12]
Rauf, K., Akinyele, A.Y., Etuk, M.O., Zubair, R.O. and Aasa, M.A. (2019) Some Results of Stability and Spectra Properties on Semigroupn of Linear Operator. Advances of Pure Mathematics, 9, 43-51. https://doi.org/10.4236/apm.2019.91003
