Orthogonality preserving infinite dimensional quadratic stochastic operators
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English English |
| Published: |
American Institute of Physics
2015
|
| Subjects: | |
| Online Access: | http://irep.iium.edu.my/44787/ http://irep.iium.edu.my/44787/ http://irep.iium.edu.my/44787/ http://irep.iium.edu.my/44787/1/mf-hasan-AIP-2015.pdf http://irep.iium.edu.my/44787/4/44787_Orthogonality%20preserving%20infinite%20dimensional%20quadratic%20stochastic%20operators_SCOPUS.pdf |
| Summary: | In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators. |
|---|