Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces
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Authors
Ting-jian Xiong
- Department of Mathematics, Sichuan University of Science & Engineering, 643000 Zigong, Sichuan, P. R. China.
Heng-you Lan
- Department of Mathematics, Sichuan University of Science & Engineering, 643000 Zigong, Sichuan, P. R. China.
Abstract
In this paper, we introduce and study a class of new modified iterative approximation processes for two finite families of
total asymptotically nonexpansive nonself mappings in hyperbolic spaces. By using generalization of Schu’s lemma and Tan-Xu’s
inequality, some important related properties of this modified iterative approximation are proposed and analyzed. Further, based
on the related properties, we prove \(\Delta\)-convergence and strong convergence of the modified iterative approximating process in
hyperbolic spaces. Because a total asymptotically nonexpansive nonself mapping in hyperbolic spaces includes asymptotically
nonexpansive mapping, (generalized) nonexpansive mapping of all normed linear spaces, Hadamard manifolds and CAT(0)
spaces as special cases, the results presented in this paper improve and generalize the corresponding results in the literature.
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ISRP Style
Ting-jian Xiong, Heng-you Lan, Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1407--1423
AMA Style
Xiong Ting-jian, Lan Heng-you, Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces. J. Nonlinear Sci. Appl. (2017); 10(4):1407--1423
Chicago/Turabian Style
Xiong, Ting-jian, Lan, Heng-you. "Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1407--1423
Keywords
- Convergence analysis
- new modified iterative approximating process
- \(\Delta\)-convergence and strong convergence
- total asymptotically nonexpansive nonself mapping
- hyperbolic space.
MSC
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