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- 2018
单调α-非扩张映象不动点的强收敛定理
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Abstract:
在一致凸Banach空间中引入偏序，介绍了一个改进的关于单调α-非扩张映象不动点的两步迭代逼近方法，在适当条件下研究了单调α-非扩张映象不动点的存在性和强收敛定理.
In this paper, a modified two-step iterative approximation method is introduced for finding a fixed point of monotone α-nonexpansive mapping in a uniformly convex ordered Banach space with a partial order. Moreover, the existence theorems and strong convergence theorems are studied about the fixed point of monotone α-nonexpansive mapping under some suitable conditions
| [1] | SONG Y S, PROMLUANG K, KUMAN P, et al. Some Convergence Theorems of the Mann Iteration for Monotone α-Nonexpansive Mappings[J]. Appl Math Comput, 2016, 287-288(S): 74-82. |
| [2] | RAN A C M. , REURINGS M C B. A Fixed Point Theorem in Partially Ordered Sets and Some Applications to Matrix Equations[J]. Proc Am Math Soc, 2003, 132(5): 1435-1443. |
| [3] | BIN DEHAISH B A, KHAMSI M A. Mann Iteration Process for Monotone Nonexpansive Mappings[J]. Fixed Point Theory and Applications, 2015, 2015(1): 177. DOI:10.1186/s13663-015-0416-0 |
| [4] | 闻道君. 广义平衡问题和渐近严格伪压缩映象的粘滞-投影方法[J]. 系统科学与数学, 2014, 34(6): 693-702. |
| [5] | ISHIKAWA S. Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space[J]. Proc Am Math Soc, 1976, 59(1): 65-71. DOI:10.1090/S0002-9939-1976-0412909-X |
| [6] | THAKUR B S, THAKUR D, POSTOLACHE M. A new Iterative Scheme for Numerical Reckoning Fixed Points of Suzuki's Generalized Nonexpansive Mappings[J]. Appl Math Comput, 2016, 275: 147-155. |
| [7] | XU H K. Inequality in Banach Spaces with Applications[J]. Nonlinear Analysis, 1991, 16(12): 1127-1138. DOI:10.1016/0362-546X(91)90200-K |
| [8] | SCHU J. Weak and Strong Convergence to Fixed Points of Asymptotically Nonexpansive Mappings[J]. Bull Aust Math Soc, 1991, 43(1): 153-159. DOI:10.1017/S0004972700028884 |
