Some classes of 2-partition geometric quadratic stochastic operator on countable state space and its regularity

Abstract

This research is designed to define and construct some classes of Geometric quadratic stochastic operator defined on the countable state space generated by 2-partition of finite and infinite points, and to investigate their trajectory behaviour. These operators can be reinterpreted in terms of evolutionary operator of free population with arbitrary initial measure. It is shown that such operators are regular transformations through the convergence of the trajectory behaviour to a fixed point in the open interval (0,1) which indicates the existence of the strong limit of the sequence of trajectories.