A class of geometric quadratic stochastic operator on countable state space and its regularity

Abstract

We have constructed a Geometric quadratic stochastic operator generated by 2-partition of singleton defined on countable state space , where . We have studied the trajectory behavior of such operator for any initial measure . It is shown that such operator converges to a fixed point which indicates the existence of the strong limit of the sequence . This follows that such operator is a regular transformation.