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Lobachevskii Journal of Mathematics

, Volume 32, Issue 4, pp 385–394 | Cite as

On a class of separable quadratic stochastic operators

  • U. A. Rozikov
  • A. Zada
Article

Abstract

The purpose of this paper is to investigate a class of separable quadratic stochastic operators. Each separable quadratic stochastic operator (SQSO) depends on two quadratic matrices A and B, which have some relations. In this paper we proved that for each skew symmetric matrix A the corresponding SQSO is a linear operator. We also proved that non linear Volterra QSOs are not SQSOs. For a fixed matrix A we also discussed some properties of the set of all the corresponding matrices B of SQSOs.

Keywords and phrases

Skew symmetric matrices Quadratic stochastic operators Volterra operators 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Institute of Mathematics and Information TechnologiesTashkentUzbekistan
  2. 2.Abdus Salam School of Mathematical Sciences (ASSMS)GCULahorePakistan
  3. 3.Department of MathematicsUniversity of PeshawarPeshawarPakistan

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