New majorization is in advantage as compared to the classical one since it can be defined as a partial order on sequences. We call it as b - order. Further, the defined order is used to establish a bistochasticity of nonlinear operators in which, in this study is restricted to the simplest case of nonlinear operators i.e quadratic operators. The discussions in this paper are based on bistochasticity of Quadratic Stochastic Operators (QSO) with respect to the b-order. In short, such operators are called b-bistochastic QSO. The main objectives in this paper are to show the construction of non-homogeneous Markov measures associated with QSO and to show the defined measures associated with the classes of b-bistochastic QSOs meet the mixing property.
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