@article{scholars20306, volume = {15}, pages = {872 - 877}, year = {2019}, doi = {10.11113/mjfas.v15n6.1423}, note = {Cited by: 10}, title = {A class of geometric quadratic stochastic operator on countable state space and its regularity}, number = {6}, journal = {Malaysian Journal of Fundamental and Applied Sciences}, publisher = {Penerbit UTM Press}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85103180228&doi=10.11113\%2fmjfas.v15n6.1423&partnerID=40&md5=1251083b7778a98ee4183c340bc92b53}, abstract = {We have constructed a Geometric quadratic stochastic operator generated by 2-partition {\ensuremath{\xi}} of singleton defined on countable state space X , where X =0,1,2,.... We have studied the trajectory behavior of such operator for any initial measure u {\ensuremath{\epsilon}} S(X, F) . It is shown that such operator converges to a fixed point which indicates the existence of the strong limit of the sequence Vn(u) . This follows that such operator is a regular transformation. {\copyright} 2019 Penerbit UTM Press. All rights reserved.}, issn = {2289599X}, author = {Karim, Siti Nurlaili and Hamzah, Nur Zatul Akmar and Ganikhodjaev, Nasir} }