R-majorizing quadratic stochastic operators: Examples on 2D simplex

A vector majorization is a preorder of dispersion for vectors with the same length and same sum of components. the vector majorization can be viewed as a preorder of distance from a uniform vector. a preorder of distance from any fixed non-uniform vector of positive components,so-called r-majorization,is a generalization of usual vector majorization. in this paper,a new class of mappings so-called r-majorizing quadratic stochastic operators was introduced. the r-majorizing quadratic stochastic operator is a generalization of a quadratic doubly stochastic operator. some relevant examples are provided. moreover,the dynamics of some non-scrambling r-majorizing quadratic stochastic operators are studied.