R−Majorizing quadratic stochastic operators: Examples on 2D simplex - Saburov, Mansoor; Yusof, Nur Atikah (Institute Mathematical Sciences, Universiti Putra Malaysia, 2016)
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.