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In this paper we propose a new viscosity approximation scheme for computing fixed points of asymptotically nonexpansive mappings in Banach spaces. Strong convergence theorem is established under some certain different control conditions of the viscosity methods for asymptotically nonexpansive mappings, and some recent results are improved and generalized.
Relatively nonexpansive mapping is a kind of important mappings which has a close connection with some problems in the area of image recovery, economics, applied mathematics and engineering sciences. Two kinds of iterative schemes, Mann and Ishikawa iterative schemes, will be investigated for approximating the fixed points of strongly relatively nonexpansive mappings in a real smooth and uniformly...
In this paper, I proved two strong convergence theorems of modified Ishikawa iteration and modified Halpern iteration for hemi-relatively nonexpansive mappings in a Banach space. The results presented in this work improve on the corresponding one announced by many others.
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