On b-bistochastic quadratic stochastic operators and their properties /
In the present thesis, we considered a majorization in term of b-order. Using such majorization, we defined bistochastic QSOs with respect to b-order, namely b-bistochastic QSOs in which it defines a new class of QSOs. Further, we provided some crucial properties of b-bistochastic QSOs in a general...
محفوظ في:
| المؤلف الرئيسي: | |
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| التنسيق: | أطروحة |
| اللغة: | English |
| منشور في: |
Kuantan, Pahang :
Kuliyyah of Science, International Islamic University Malaysia,
2016
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| الموضوعات: | |
| الوصول للمادة أونلاين: | Click here to view 1st 24 pages of the thesis. Members can view fulltext at the specified PCs in the library. |
| الوسوم: |
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| الملخص: | In the present thesis, we considered a majorization in term of b-order. Using such majorization, we defined bistochastic QSOs with respect to b-order, namely b-bistochastic QSOs in which it defines a new class of QSOs. Further, we provided some crucial properties of b-bistochastic QSOs in a general setting, and fully described b-bistochastic QSOs on one and two dimensional simplices. In addition, we showed that for every b-bistochastic QSOs, their trajectories were convergent. Besides, it was found that (0,0,…,1) was the fixed point of any b-bistochastic QSOs. Next, we managed to fully study the dynamics of b-bistochatic QSOs on one dimensional simplex, whereas on two dimensional simplex, we limited the study on boundaries only. Generally, it was established that the set of all b-bistochastic QSOs formed a convex set, hence we were interested to describe its extreme points. The results were presented as the list of extreme points on low dimensional simplices. Moreover, we introduced quasi-extremity of b-bistochastic QSO and investiged it on two dimensional simplex. Finally, we associated Markov measures with b-bistochastic QSOs. On some classes of b-bistochastic QSOs, the defined measures were proven to satisfy the mixing property. Moreover, we studied the absolute continuity of Markov measures associated with a class of b-bistochastic QSOs. |
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| وصف مادي: | xi, 103 leaves : ill. ; 30cm. |
| بيبلوغرافيا: | Includes bibliographical references (leaves 98-102). |