Banach operator pairs, common fixed-points, invariant approximations, and \(*\)-nonexpansive multimaps

DOI10.1016/J.NA.2007.08.047zbMath1170.47034OpenAlexW2008270055MaRDI QIDQ949696

Naseer Shahzad, M. A. Al-Thagafi

Publication date: 21 October 2008

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.2007.08.047

zbMATH Keywords

normed spaceinvariant approximationBanach operator paircommon fixed-point\(*\)-nonexpansive multimap\(C_q\)-commuting pair\(I\)-nonexpansive mapciric type map

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (12)

Common fixed points of ordered \(g\)-contractions in partially ordered metric spaces ⋮ Common fixed point and approximation results for generalized \((f, g)\)-weak contractions ⋮ Some common fixed point and invariant approximation results for nonexpansive mappings in convex metric space ⋮ Some common fixed point theorems for generalized nonlinear contractive mappings ⋮ Common fixed points of a generalized ordered \(g\)-quasicontraction in partially ordered metric spaces ⋮ Invariant approximation results via common fixed point theorems for generalized weak contraction maps ⋮ Common fixed point and invariant approximation results ⋮ Banach operator pair and common fixed points for nonexpansive maps ⋮ Some common fixed point theorems for Banach operator pairs with applications in best approximation ⋮ Some common fixed-point and invariant approximation results with generalized almost contractions ⋮ Common fixed points, invariant approximation and generalized weak contractions ⋮ Best simultaneous approximations, asymptotically nonexpansive mappings and variational inequalities in Banach spaces

Cites Work

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• Fixed point theorems and invariant approximations
• A note on fixed-point theorems
• Common fixed points of noncommuting mappings
• Common fixed points and best approximation
• Common fixed-points for Banach operator pairs in best approximation
• Noncommuting selfmaps and invariant approximations
• Common Fixed Point Theorems for Commuting Maps on a Metric Space
• A Generalization of Banach's Contraction Principle
• Fixed Point Theorems for Non-Expansive Mappings on Star-Shaped Subsets of Banach Spaces
• Invariant Approximations for GeneralizedI-Contractions
• Invariant approximations and \(R\)-subweakly commuting maps

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