$\mathbf{p}$-Majorizing quadratic stochastic operators

In this paper, we introduce a new class of the so-called $\mathbf{p}$-majorizing quadratic stochastic operators which is the generalization of the class of quadratic doubly stochastic operators. We provide a criterion for the regularity of $\mathbf{p}$-majorizing quadratic stochastic operators acting on 2D simplex. Some relevant examples are also provided.