A hybrid iterative scheme for asymptotically \(k\)-strict pseudo-contractions in Hilbert spaces

DOI10.1016/j.na.2008.02.090zbMath1309.47079OpenAlexW1970338722MaRDI QIDQ1001862

Yeol Je Cho, Meijuan Shang, Xiaolong Qin, Kang, Shin Min

Publication date: 19 February 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.02.090

zbMATH Keywords

fixed pointnonexpansive mappingstrict pseudo-contractionasymptotically \(k\)-strict pseudo-contraction

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

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Cites Work

• Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• An example concerning fixed points
• Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Iterative methods for strict pseudo-contractions in Hilbert spaces
• Strong convergence of the CQ method for fixed point iteration processes
• Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups
• Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
• Mean Value Methods in Iteration