Fixed point theory in cone metric spaces obtained via the scalarization method

DOI10.1016/j.camwa.2010.03.046zbMath1197.54055OpenAlexW1974953214MaRDI QIDQ710963

Majid Fakhar, Alireza Amini-Harandi

Publication date: 23 October 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.03.046

zbMATH Keywords

fixed pointordered Banach spacecone metric spacescalarization method

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (36)

Caristi's fixed point theorem in cone metric space ⋮ Variational analysis in cone pseudo-quasimetric spaces and applications to group dynamics ⋮ Unnamed Item ⋮ Fixed point theorems of generalized contraction mappings on \(\varpi\)-cone metric spaces over Banach algebras ⋮ Generalized fractal transforms and self-similar objects in cone metric spaces ⋮ Mizoguchi-Takahashi-type theorems in tvs-cone metric spaces ⋮ Fixed point theorems for set-valued contractions ⋮ Some fixed and periodic points in abstract metric spaces ⋮ On the metrizability of cone metric spaces ⋮ Partially ordered cone metric spaces and coupled fixed point results ⋮ A note on tvs-cone metric fixed point theory ⋮ Some remarks on Perov type mappings in cone metric spaces ⋮ On \(w\)-compatible mappings and common coupled coincidence point in cone metric spaces ⋮ A note on Stone's, Baire's, Ky Fan's and Dugundji's theorem in tvs-cone metric spaces ⋮ On cone metric spaces: a survey ⋮ On an equivalence of topological vector space valued cone metric spaces and metric spaces ⋮ A framework to combine vector-valued metrics into a scalar-metric: application to data comparison. ⋮ Coupled fixed point theorems under weak contractions ⋮ Fixed points and endpoints of set-valued contractions in cone metric spaces ⋮ Remarks on some recent fixed point results on quaternion-valued metric spaces ⋮ Fixed point theorem of generalized operator quasi-contractive mapping in cone metric space ⋮ Common fixed points for nonlinear quasi-contractions of Ćirić type ⋮ Fixed points of Geraghty-type mappings in various generalized metric spaces ⋮ Dual Kadec-Klee property and fixed points ⋮ A unified theory of cone metric spaces and its applications to the fixed point theory ⋮ On the scalarization method in cone metric spaces ⋮ Boyd-Wong-type common fixed point results in cone metric spaces ⋮ Coupled coincidence points in partially ordered cone metric spaces with a \(c\)-distance ⋮ Iterative approximation of fixed points of quasi-contraction mappings in cone metric spaces ⋮ A note on fixed point results in complex-valued metric spaces ⋮ Some results on fixed points of multifunctions on abstract metric spaces ⋮ Some equivalences between cone \(b\)-metric spaces and \(b\)-metric spaces ⋮ Unnamed Item ⋮ Common fixed point results of Perov type contractive mappings in \(D^\ast\)-cone metric spaces ⋮ Various generalizations of metric spaces and fixed point theorems ⋮ A note on the equivalence of some metric and \(H\)-cone metric fixed point theorems for multivalued contractions

Cites Work

• Some new common fixed point theorems under strict contractive conditions
• Cone metric spaces and fixed point theorems of contractive mappings
• Jungck's common fixed point theorem and E.A property
• Some notes on the paper ``Cone metric spaces and fixed point theorems of contractive mappings
• Some extensions of Banach's contraction principle in complete cone metric spaces
• Endpoints and fixed points of set-valued contractions in cone metric spaces
• Quasi-contraction on a cone metric space
• Fixed and periodic point results in cone metric spaces
• \(\varphi\)-pairs and common fixed points in cone metric spaces
• Common fixed point theorems for weakly compatible pairs on cone metric spaces
• Some common fixed point results in cone metric spaces
• Common fixed points of two maps in cone metric spaces
• Weakly \(\varphi \)-pairs and common fixed points in cone metric spaces
• A solvability theorem for a class of quasiconvex mappings with applications to optimization
• General Ekeland's variational principle for set-valued mappings.
• Common fixed point results for noncommuting mappings without continuity in cone metric spaces
• Common fixed points for maps on cone metric space
• Ordered linear spaces
• Common Fixed Point Theorems for Commuting Maps on a Metric Space
• A Generalization of Banach's Contraction Principle
• On Contractive Mappings

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