Fixed point theorems for asymptotically nonexpansive mappings
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Publication:4306597
DOI10.1016/0362-546X(94)90116-3zbMath0812.47058OpenAlexW2091087115MaRDI QIDQ4306597
Publication date: 9 May 1995
Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0362-546x(94)90116-3
fixed pointuniformly normal structureweakly compact convex subsetBanach space with a weakly continuous duality mapMaluta constant
Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Strong convergence theorems for resolvents of accretive operators in Banach spaces
- Normal structure coefficients for Banach spaces
- Uniformly normal structure and related coefficients
- Maluta's question on sequence coefficients in Banach spaces
- Nonstandard methods in fixed point theory
- On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak \(\omega\)-limit set
- Banach spaces which are nearly uniformly convex
- Convergence theorems for sequences of nonlinear operators in Banach spaces
- Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure
- Nonexpansive Mappings, Asymptotic Regularity and Successive Approximations
- A Generalization of Uniformly Rotund Banach Spaces
- Existence and convergence for fixed points of mappings of asymptotically nonexpansive type
- A fixed point theorem on k-uniformly rotund spaces
- A Fixed Point Theorem for Mappings which do not Increase Distances
- Weak convergence of the sequence of successive approximations for nonexpansive mappings
- A Fixed Point Theorem for Asymptotically Nonexpansive Mappings