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

## DOI:

https://doi.org/10.11113/mjfas.v15n6.1423## Keywords:

Singleton, Countable State Space, Quadratic Stochastic Operator, Regular Transformation## 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.

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