A note on implicit and explicit Mann iterative processes for asymptotically \(\phi\)-strongly pseudocontractive mappings

DOI10.1155/2012/912050zbMath1366.47020OpenAlexW1972083524WikidataQ58906928 ScholiaQ58906928MaRDI QIDQ443130

Yonghong Yao, Luigi Muglia

Publication date: 6 August 2012

Published in: Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/912050

zbMATH Keywords

strong convergenceuniformly smooth Banach spaceasymptotically \(\phi\)-strongly pseudocontractive mappingsexplicit Mann iterative processmodified implicit iterative process

Mathematics Subject Classification ID

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

Related Items

On best proximity point theorems and fixed point theorems for \(p\)-cyclic hybrid self-mappings in Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Iterative approximation of fixed points for asymptotically strict pseudocontractive type mappings in the intermediate sense
• Iterative construction of fixed points of asymptotically nonexpansive mappings
• Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces
• The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption
• The new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings
• Equivalence theorems of the convergence between Ishikawa and Mann iterations with errors for generalized strongly successively \(\Phi \)-pseudocontractive mappings without Lipschitzian assumptions
• Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces
• Asymptotically strict pseudocontractive mappings in the intermediate sense
• Ishikawa and Mann iterative processes with error for nonlinear strongly accretive operator equations
• Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings.
• Zeros of accretive operators
• Approximate fixed point sequences and convergence theorems for asymptotically pseudocontractive mappings.
• Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
• Iterative solution of nonlinear equations of the \(\Phi\)-strongly accretive type
• Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space
• Geometric properties of Banach spaces and nonlinear iterations
• On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings
• EQUILIBRIUM POINTS FOR A SYSTEM INVOLVING M-ACCRETIVE OPERATORS
• Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings
• NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
• Convergence theorem for zeros of generalized Lipschitz generalized phi-quasi-accretive operators