Kohlenbach双曲空间中一类广义拟压缩映象的收敛速度
Rates of convergence for a class of generalized quasi contractive mappings in Kohlenbach hyperbolic spaces
摘要：
本文是对广义拟压缩算子研究的继续，主要是由于Akhtar等人[A multi-step implicit itative iterative process for common不动点of generalized C^{q}-operators in凸度量空间，Sci.内部：25（4）（2013），887-891]，在非正截面曲率的空间中。我们的目标是建立有关的经典迭代算法，如Picard，Mann，Ishikawa和Xu-Noor迭代算法的收敛特性的结果与建议的广义拟压缩算子类。此外，我们采用Berinde [Comparing Krasnosel'skii and Mann迭代法for Lipschitz广义伪压缩，Int. Conference on不动点Theory Appl.，15-26，横滨出版社，横滨，2004年。]在这样的空间设置中，比较这些迭代算法的相应收敛速率。本文的结果改进和推广了文献中的一些最近的相应结果。
英文摘要：
This paper is a continuation to the study of generalized quasi contractive operators, essentially due to Akhtar et al. [A multi-step implicit iterative process for common fixed points of generalized C^{q}-operators in convex metric spaces, Sci. Int., 25(4) (2013), 887-891], in spaces of nonpositive sectional curvature. We aim to establish results concerning convergence characteristics of the classical iterative algorithms such as Picard, Mann, Ishikawa and Xu-Noor iterative algorithms associated with the proposed class of generalized quasi contractive operators. Moreover, we adopt the concept introduced by Berinde [Comparing Krasnosel'skii and Mann iterative methods for Lipschitzian generalized pseudo-contractions, Int. Conference on Fixed Point Theory Appl., 15-26, Yokohama Publ., Yokohama, 2004.] for a comparison of the corresponding rates of convergence of these iterative algorithms in such setting of spaces. The results presented in this paper improve and extend some recent corresponding results in the literature.
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