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1.
Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces 总被引:1,自引:0,他引:1
In this paper, we modify Halpern and Mann’s iterations for finding a fixed point of a relatively nonexpansive mapping in a Banach space. Consequently, a strong convergence theorem for a nonspreading mapping is deduced. Using a concept of duality theorems, we also obtain analogue results for certain generalized nonexpansive and generalized nonexpansive type mappings. Finally, we discuss two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a Banach space. 相似文献
2.
Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications 总被引:1,自引:0,他引:1
Yongfu Su Hong-kun Xu Xin Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(12):3890-3906
The purpose of this article is to prove strong convergence theorems for common fixed points of two countable families of weak relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems, the monotone hybrid algorithms are presented and are used to approximate the common fixed points. Using this result, we also discuss the problem of strong convergence concerning the maximal monotone operators in a Banach space. The results of this article modify and improve the results of Matsushita and Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory 134 (2005) 257-266] and the results of Plubtieng and Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space, J. Approx. Theory 149 (2007) 103-115] and the results of Su et al. [Y. Su, Z. Wang and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009) 5616-5628], and many others. 相似文献
3.
Somyot Plubtieng 《Journal of Approximation Theory》2007,149(2):103-115
In this paper, we establish strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space by using the hybrid method in mathematical programming. Our results extend and improve the recent ones announced by Matsushita and Takahashi [A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory 134 (2005) 257-266], Matinez-yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411], and many others. 相似文献
4.
Weerayuth Nilsrakoo 《Applied mathematics and computation》2009,214(2):595-606
This paper is concerned with convergence of an approximating common fixed point sequence of countable Lipschitzian mappings in a uniformly convex Banach space. We introduce a new condition for a class of mappings to obtain several weak and strong convergence theorems. This new condition is implied by many previous known conditions introduced by many authors. We also apply our results for a class of nonexpansive mappings and asymptotically nonexpansive mappings and we immediately obtain convergence theorems proved by Song-Chen, Kimura-Takahashi, Tan-Xu, and many others. 相似文献
5.
Yongfu Su Ziming Wang Hongkun Xu 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5616-5628
The purpose of this article is to prove strong convergence theorems for common fixed points of two closed hemi-relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems, the monotone hybrid algorithms are presented and are used to approximate the common fixed points. Finally, a new simplified hybrid algorithm has been proposed and relative convergence theorem has been proved by using the new method for proofs. The results of this article modify and improve the results of Matsushita, Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory 134 (2005) 257–266] and the results of Plubtieng, Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space, J. Approx. Theory 149 (2007) 103–115], and many others. 相似文献
6.
In this paper, we prove three strong convergence theorems of modified Mann iteration for relatively asymptotically nonexpansive mappings, relatively nonexpansive mappings, and maximal monotone operators in a Banach space, respectively. Our results extend and improve the recent ones announced by Nakajo, Takahashi, Matsushita, Kim, Martinez-Yanex, Xu, and some others. 相似文献
7.
In this paper, we prove a strong convergence theorem of modified Ishikawa iterations for relatively asymptotically nonexpansive
mappings in Banach space. Our results extend and improve the recent results by Nakajo, Takahashi, Kim, Xu, Matsushita and
some others. 相似文献
8.
9.
Hossein Dehghan 《Applied Mathematics Letters》2011,24(9):1584-1587
In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence theorem due to Matsushita and Takahashi [S. Matsushita, W. Takahashi, Approximating fixed points of nonexpansive mappings in a Banach space by metric projections, Appl. Math. Comput. 196 (2008) 422–425] which was established for nonexpansive mappings. 相似文献
10.
弱相对非扩张映像不动点单调CQ算法与应用 总被引:2,自引:1,他引:1
Kamimura和Takahashi$^{[7]}$证明了相对非扩张映像CQ迭代算法的强收敛定理.该文构造了单调CQ算法, 用来逼近弱相对非扩张映像不动点, 证明了强收敛定理. 并将结果应用于逼近Banach空间极大单调算子的零点. 单调CQ算法比目前的CQ算法收敛速度快. 另外, 为证明弱相对非扩张映像不动点强收敛定理,该文运用了新的Cauchy列证明方法, 而不用Kadec-Klee性质, 该文结果改进了S.Matsushita 和 W.Takahashi及其它人的结果. 相似文献