R-majorizing operators: 2D simplex - Saburov, Mansoor; Yusof, Nur Atikah (2014)
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 pre-order of distance from a uniform vector. A pre-order of distance from any fixed vector of positive components, so-called r-majorization, is a generalization of usual vector majorization. In this paper, we introduce a new class of quadratic stochastic operators. These are called quadratic stochastic r-majorizing operators. The r-majorizing quadratic stochastic operator is a generalization of a quadratic doubly stochastic operator. We study ergodicity and regularity of quadratic stochastic r-majorizing operators.