Official thesis title: Some problems about random operator equations
1. Full name: Tạ Ngọc Ánh
2. Sex: Male
3. Date of birth:19/09/1981
4. Place of birth: BacGiang
5. Admission decision number: No 2385/SĐH dated 29/06/2007 and No 4089/SĐH dated 01/11/2007
6. Changes in academic process: Assessment Council thesis at the grassroots level decided to rename the thesis title from "Some problems about random equations" to "Some problems about random operator equations".
7. Official thesis title: Some problems about random operator equations
8. Major: Theory of probability and mathematical statistics
9. Code: 62 46 15 01
10. Supervisors: Prof. Dr.sc. Đặng Hùng Thắng
11. Summary of the new findings of the thesis
The thesis proved that if a random operator equation has a deterministic solution with probability one and random operators are measurable, defined in a completely separable metric space, then the random operator equation has a random solution. The thesis gave out some sufficient conditions that ensure the existence of solutions of some random operator equations.
The thesis proved some general random fixed point theorems which extended many general random fixed point theorems of many authors before. The thesis showed that if a random operator is measurable, defined in a completely separable metric space and has a deterministic fixed point with probability one, then it has a random fixed point. In order to illustrate for general random fixed point theorems, the thesis proved random versions of some fixed point theorems in the deterministic analysis. The thesis also proposed the notion of best random proximity point and proved some sufficient conditions for a random operator having a best random proximity point.
The thesis proposed the notion of completely random operator and proved some fixed point theorems for contraction and probabilistic contraction. The thesis also proved the existence of solutions of some equations of completely random operators.
12. Practical applicability, if any:
The results are meaningful in the theoretical study of random operator equations.
