Strong convergence theorems with a Noor-type iterative scheme in convex metric spaces

DOI10.1016/j.camwa.2011.04.017zbMath1393.47032OpenAlexW2066363000MaRDI QIDQ640523

Byung-Soo Lee

Publication date: 18 October 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.04.017

zbMATH Keywords

strong convergenceconvex metric spaceasymptotically \(f\)-expansive mappingasymptotically quasi-\(f\)-expansive mapping\(f\)-expansive mapping\(f\)-uniformly quasi-\(sup(f)\)-Lipschitzian mappingNoor-type iteration

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15) Special maps on metric spaces (54E40)

Related Items

Convergence of a general algorithm of asymptotically nonexpansive maps in uniformly convex hyperbolic spaces ⋮ The convergence of three-step iterative schemes for generalized \(\Phi\)-hemi-contractive mappings and the comparison of their rate of convergence ⋮ Some Boyd-Wong contraction type mappings in \(b\)-metric spaces ⋮ Common fixed points for \((\psi -\varphi)\)-weak contractions type in \(b\)-metric spaces

Cites Work

• Stronger convergence theorems for an infinite family of uniformly quasi-Lipschitzian mappings in convex metric spaces
• Convergence of an Ishikawa type iterative scheme for asymptotically quasi-nonexpansive mappings
• Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications
• The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces
• Three-step methods for nonexpansive mappings and variational inequalities
• Convergence of three-step iterations for asymptotically nonexpansive mappings
• Approximating the common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex metric spaces
• Convergence of a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications
• Convergence theorems for fixed points of uniformly quasi-Lipschitzian mappings in convex metric spaces
• Extended general variational inequalities
• Approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces
• Some aspects of variational inequalities
• New approximation schemes for general variational inequalities
• Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces
• Some developments in general variational inequalities
• Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces
• Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings
• Unnamed Item