A stationary point theorem characterizing metric completeness

DOI10.1016/j.aml.2010.08.039zbMath1295.54056OpenAlexW2069789839MaRDI QIDQ609980

Jacek R. Jachymski

Publication date: 1 December 2010

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

Full work available at URL: https://doi.org/10.1016/j.aml.2010.08.039

zbMATH Keywords

fixed pointset-valued mappingstationary pointpartial ordermetric completeness

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Complete metric spaces (54E50) Fixed-point and coincidence theorems (topological aspects) (54H25)

Related Items (8)

Endpoints of multivalued nonexpansive mappings in geodesic spaces ⋮ Fixed point and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces ⋮ Approximating common endpoints of multivalued generalized nonexpansive mappings in hyperbolic spaces ⋮ Fixed points and completeness in metric and generalized metric spaces ⋮ Unnamed Item ⋮ Multi-valued graph contraction principle with applications ⋮ Some asymptotic stationary point theorems in topological spaces ⋮ Unnamed Item

Cites Work

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• Cone uniform, cone locally convex and cone metric spaces, endpoints, set-valued dynamic systems and quasi-asymptotic contractions
• Existence and uniqueness of endpoints of closed set-valued asymptotic contractions in metric spaces
• Generalized contractions of Meir-Keeler type, endpoints, set-valued dynamical systems and generalized pseudometrics in uniform spaces
• Endpoints of set-valued contractions in metric spaces
• On the order-theoretic Cantor theorem
• On the variational principle
• Endpoints of set-valued dynamical systems of asymptotic contractions of Meir-Keeler type and strict contractions in uniform spaces
• The uniqueness of endpoints for set-valued dynamical systems of contractions of Meir-Keeler type in uniform spaces
• Endpoint theory for set-valued nonlinear asymptotic contractions with respect to generalized pseudodistances in uniform spaces
• Quasi-asymptotic contractions, set-valued dynamical systems, uniqueness of endpoints and generalized pseudodistances in uniform spaces
• Shorter Notes: A Characterization of Metric Completeness

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