On b-bistochastic quadratic stochastic operators

Abstract

In the present paper we introduce a new notion of order called b-order. Then we define a bistochasticity quadratic stochastic operator (q.s.o.) with respect to the b-order, and call it a b-bistochastic q.s.o. We include several properties of the b-bistochastic q.s.o. and descriptions of all b-bistochastic q.s.o. defined on a two dimensional simplex.