New fixed point theorems for 1-set-contractive operators in Banach spaces

DOI10.1016/j.na.2006.06.051zbMath1124.47038OpenAlexW2053484131MaRDI QIDQ881624

Shaoyuan Xu

Publication date: 30 May 2007

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.2006.06.051

zbMATH Keywords

fixed point theoremstopological degreereal Banach spacessemi-closed \(1\)-set-contractive operators

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (10)

Fixed Point Theorem and Related Nonlinear Analysis by the Best Approximation Method in p-Vector Spaces ⋮ Measures of weak noncompactness and fixed point theory for 1-set weakly contractive operators on unbounded domains ⋮ The fixed point theorems of 1-set-contractive operators in Banach space ⋮ 1-set-contractive perturbations of accretive operators in Menger PN-spaces ⋮ Nonlinear analysis in \(p\)-vector spaces for single-valued 1-set contractive mappings ⋮ Minimum selections and fixed points of set-valued operators in Banach spaces with some uniform convexity ⋮ The Chebyshev selections and fixed points of set-valued mappings in Banach spaces with some uniform convexity ⋮ Topological degree for 1-set-contractive fields in M-PN spaces and its applications ⋮ Generalizations of fixed-point theorems of Altman and Rothe types ⋮ Nonlinear analysis by applying best approximation method in \(p\)-vector spaces

Cites Work

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• Random fixed points for several classes of 1-ball-contractive and 1-set-contractive random maps
• Degree theory for local condensing maps
• Remarks on condensing and \(k\)-set-contractive mappings
• The Fixed-Point Index and the Fixed-Point Theorems of 1-Set-Contraction Mappings
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• Random Approximations and Random Fixed Point Theorems for Continuous 1-Set- Contractive Random Maps
• The fixed point index and asymptotic fixed point theorems for $k$-set-contractions
• Approximation theorems and fixed point theorems for various classes of 1-set-contractive mappings in Banach spaces

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