A class of geometric quadratic stochastic operator on countable state space and its regularity - Karim, Siti Nurlaili; Hamzah, Nur Zatul Akmar; Ganikhodjaev, Nasir (Penerbit UTM Press, 2019)
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.