Some fixed point results for relation theoretic weak \(\varphi \)-contractions in cone metric spaces equipped with a binary relation and application to the system of Volterra type equations

DOI10.1007/s11117-019-00719-8zbMath1440.54044OpenAlexW2990431032MaRDI QIDQ2194074

Satish Shukla, Nikita Dubey

Publication date: 25 August 2020

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-019-00719-8

zbMATH Keywords

integral equationfixed pointtransitive relationcone metric spacerelation theoretic weak \(\varphi \)-contraction

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) Special maps on metric spaces (54E40) Volterra integral equations (45D05)

Related Items

New fixed point theorems for set-valued contractions in \(b\)-metric spaces ⋮ Iterated function systems consisting of generalized convex contractions in the framework of complete strong \(b\)-metric spaces ⋮ Fixed point theorems in graphical cone metric spaces and application to a system of initial value problems ⋮ A unified Feng-Liu type result in relational metric spaces with an application

Cites Work

• Unnamed Item
• Unnamed Item
• Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality
• Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in \(G\)-metric spaces
• Fixed point results under c-distance in tvs-cone metric spaces
• Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings
• Linear contractions in product ordered metric spaces
• Ordered cone metric spaces and fixed point results
• On cone metric spaces: a survey
• Cone metric spaces and fixed point theorems of contractive mappings
• Relation-theoretic contraction principle
• Common fixed point theorems for weakly compatible pairs on cone metric spaces
• Common fixed points of two maps in cone metric spaces
• Remarks on ``Quasi-contraction on a cone metric space
• Fixed point results for weak \(\varphi\)-contractions in cone metric spaces over Banach algebras and applications
• Some remarks on Perov type mappings in cone metric spaces
• Some results of Perov type in rectangular cone metric spaces
• Fixed point in topological vector space-valued cone metric spaces
• New fixed point results for \(E\) -metric spaces
• The Ran-Reurings fixed point theorem without partial order: a simple proof
• Common fixed points in cone metric spaces
• Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations
• Some topological properties and fixed point results in cone metric spaces over Banach algebras
• Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications
• A fixed point theorem in partially ordered sets and some applications to matrix equations
• Nonlinear contractions in metric spaces under locally T-transitive binary relations
• A new survey: Cone metric spaces
• Nieto-Lopez theorems in ordered metric spaces