Viscosity Methods of Asymptotically Pseudocontractive and Asymptotically Nonexpansive Mappings for Variational Inequalities [PDF]
Abstract and Applied Analysis, 2012 Let {𝑡𝑛}⊂(0,1) be such that 𝑡𝑛→1 as 𝑛→∞, let 𝛼 and 𝛽 be two positive numbers such that 𝛼+𝛽=1, and let 𝑓 be a contraction. If 𝑇 be a continuous asymptotically pseudocontractive self-mapping of a nonempty bounded closed convex subset 𝐾 of a real reflexive ...
Xionghua Wu +3 more
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Strong convergence theorems for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups [PDF]
Fixed Point Theory and Applications, 2006 AbstractStrong convergence theorems are obtained from modified Halpern iterative scheme for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups, respectively. Our results extend and improve the recent ones announced by Nakajo, Takahashi, Kim, Xu, and some others.
Xiaolong Qin, Yongfu Su
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Fixed points of asymptotically regular nonexpansive mappings on nonconvex sets [PDF]
Abstract and Applied Analysis, 2003 It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci:1≤i≤n } of X, and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then ...
Wieslawa Kaczor
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Computational and Mathematical MethodsIt is our aim to propose a new iterative algorithm with an inertial term involving asymptotically nonexpansive mapping in the framework of Hilbert spaces.
Emmanuel Akaligwo +4 more
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Approximation of fixed points of asymptotically nonexpansive mappings [PDF]
Proceedings of the American Mathematical Society, 1991 Let T T be an asymptotically nonexpansive self-mapping of a non-empty closed, bounded, and starshaped (with respect to zero)
Jürgen Schu
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Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings [PDF]
Abstract and Applied Analysis, 2009 We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space.
Watcharaporn Cholamjiak, Suthep Suantai
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Robustness of Krasnoselski-Mann's Algorithm for Asymptotically Nonexpansive Mappings [PDF]
ISRN Mathematical Analysis, 2011 Iterative approximation of fixed points of nonexpansive mapping is a very active theme in many aspects of mathematical and engineering areas, in particular, in image recovery and signal processing. Because the errors usually occur in few places, it is necessary to show that whether the iterative algorithm is robust or not. In the present work, we prove
Tang, Yu-Chao, Liu, Li-Wei
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Axioms, 2021 In this work, we introduce a new inertial accelerated Mann algorithm for finding a point in the set of fixed points of asymptotically nonexpansive mapping in a real uniformly convex Banach space.
Murtala Haruna Harbau +3 more
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Abstract and Applied Analysis, 2012 We introduce an algorithm for solving the split common fixed point problem for quasi-total asymptotically nonexpansive uniformly Lipschitzian mapping in Hilbert spaces.
Jing Na, Lin Wang, Zhaoli Ma
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Strong Convergence Theorems for Modifying Halpern Iterations for Quasi--Asymptotically Nonexpansive Multivalued Mapping in Banach Spaces with Applications [PDF]
Journal of Applied Mathematics, 2012 An iterative sequence for quasi--asymptotically nonexpansive multivalued mapping for modifying Halpern's iterations is introduced. Under suitable conditions, some strong convergence theorems are proved.
Li Yi
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