论文标题
在修改后的Halpern和Tikhonov-Mann迭代中
On modified Halpern and Tikhonov-Mann iterations
论文作者
论文摘要
我们表明，由于T.-H。 Kim和H.-K。 Xu并由A. cuntavenapit和B. Panyanak以及H. Cheval和L.Leuştean引入的Tikhonov-Mann迭代进一步研究，作为Y. Yao等人迭代的概括。 Boţ等人最近对此进行了研究。可以在一般的大地测量设置中彼此减少。特别是，这给了Boţ等人的收敛结果新证明。以及从希尔伯特（Hilbert）到猫（0）空间的概括。此外，可以将渐近规律性和基本差的定量速率调整并转化为Tikhonov-Mann迭代的速率，与H. Cheval，L。Leuştean和B. dinis的H. Cheval的最新定量结果相对应，分别为P. Pinto。在匡威方向上也是可能的。我们还为改良的Halpern（尤其是Halpern Iteration）和Tikhonov-Mann迭代的渐近$ O（1/N）$（1/N）$的渐近规则性率和特殊选择的Tikhonov-Mann迭代率。
We show that the asymptotic regularity and the strong convergence of the modified Halpern iteration due to T.-H. Kim and H.-K. Xu and studied further by A. Cuntavenapit and B. Panyanak and the Tikhonov-Mann iteration introduced by H. Cheval and L. Leuştean as a generalization of an iteration due to Y. Yao et al. that has recently been studied by Boţ et al. can be reduced to each other in general geodesic settings. This, in particular, gives a new proof of the convergence result in Boţ et al. together with a generalization from Hilbert to CAT(0) spaces. Moreover, quantitative rates of asymptotic regularity and metastability due to K. Schade and U. Kohlenbach can be adapted and transformed into rates for the Tikhonov-Mann iteration corresponding to recent quantitative results on the latter of H. Cheval, L. Leuştean and B. Dinis, P. Pinto respectively. A transformation in the converse direction is also possible. We also obtain rates of asymptotic regularity of order $O(1/n)$ for both the modified Halpern (and so in particular for the Halpern iteration) and the Tikhonov-Mann iteration in a general geodesic setting for a special choice of scalars.
