Fixed point theorem for generalized \(\varPhi \)-pseudocontractive mappings

DOI10.1016/j.na.2008.03.006zbMath1207.47059OpenAlexW2068540717MaRDI QIDQ1004624

Chang-He Xiang

Publication date: 11 March 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.2008.03.006

zbMATH Keywords

fixed pointstrongly pseudocontractive mapping\(\phi\)-strongly pseudocontractive mappinggeneralized \(\varPhi \)-pseudocontractive mapping

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

The convergence of implicit Mann and Ishikawa iterations for weak generalized \({\varphi}\)-hemicontractive mappings in real Banach spaces ⋮ The structure of fixed-point sets of Lipschitzian type semigroups ⋮ On the convergence of iterative processes for generalized strongly asymptotically \(\phi\)-pseudocontractive mappings in Banach spaces ⋮ On the convergence of Mann and Ishikawa iterative processes for asymptotically \(\phi\)-strongly pseudocontractive mappings ⋮ Necessary and sufficient condition for Mann iteration converges to a fixed point of Lipschitzian mappings ⋮ Generalized strongly nonlinear implicit quasivariational inequalities

Cites Work

• Convergence theorems for fixed points of uniformly continuous generalized \(\varPhi\)-hemi-contractive mappings
• Zeros of accretive operators
• Iterative solution of nonlinear equations of the \(\Phi\)-strongly accretive type
• Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions in Banach spaces
• Iterative solutions of nonlinear φ-strongly accretive operator equations in arbitrary Banach spaces
• Approximation methods for nonlinear operator equations
• Convergence theorems for \(\phi\)-strongly accretive and \(\phi\)-hemicontractive operators
• Iterative solution of nonlinear equations involving set-valued uniformly accretive operators.