Convergence Analysis of Best Proximity Point Problems and Split Problems for Demicontractive Operators with Applications
This dissertation consists of the two main results which are the study of best proximity point problems and split problems for demicontractive operators. To achieve the first result, we introduce a general Mann algorithm for nonself nonexpansive mappings and then prove weak and strong convergence...
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| Format: | Theses and Dissertations |
| Language: | English |
| Published: |
เชียงใหม่ : บัณฑิตวิทยาลัย มหาวิทยาลัยเชียงใหม่
2020
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| Online Access: | http://cmuir.cmu.ac.th/jspui/handle/6653943832/69544 |
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| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | This dissertation consists of the two main results which are the study of best proximity
point problems and split problems for demicontractive operators. To achieve the
first result, we introduce a general Mann algorithm for nonself nonexpansive mappings
and then prove weak and strong convergence of the proposed algorithm under some suitable
conditions in Hilbert spaces. Furthermore, we also provide numerical experiments
to illustrate the convergence behavior of our proposed algorithm. To achieve the second
result, we construct three self-adaptive algorithms with inertial effects for solving the split
problems for demicontractive operators. Under some suitable conditions, the weak and
strong convergence of the algorithms are obtained. Numerical results of image restoration
problems illustrate that these proposed algorithms are efficient and outperform other
ones. |
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