Regularity of Geometric quadratic stochastic operator generated by 2-partition of infinite points

Abstract

In this research, we construct a class of quadratic stochastic operator called Geometric quadratic stochastic operator generated by arbitrary 2-partition  of infinite points on a countable state space , where . We also study the limiting behavior of such operator by proving the existence of the limit of the sequence  through the convergence of the trajectory to a unique fixed point. It is established that such operator is a regular transformation.