A generalization of Geraghty's theorem in partially ordered metric spaces and applications to ordinary differential equations

DOI10.1186/1687-1812-2012-74zbMath1278.54031OpenAlexW2152296459WikidataQ59289680 ScholiaQ59289680MaRDI QIDQ372105

Maryam Ramezani, Saeideh Pirbavafa, Yeol Je Cho, Madjid Eshaghi-Gordji

Publication date: 11 October 2013

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1812-2012-74

zbMATH Keywords

contractionfixed pointinitial-value problempartially ordered metric spaces

Mathematics Subject Classification ID

Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces (54F05) Initial-boundary value problems for second-order parabolic equations (35K20) Fixed-point and coincidence theorems (topological aspects) (54H25) Special maps on metric spaces (54E40)

Related Items

Fixed point theorems with generalized altering distance functions in partially ordered metric spaces via \(w\)-distances and applications ⋮ Common fixed point theorems for Geraghty's type contraction mappings using the monotone property with two metrics ⋮ Fixed point theorems for asymptotically \(T\)-regular mappings in preordered modular \(G\)-metric spaces applied to solving nonlinear integral equations ⋮ A new class of contraction in \(b\)-metric spaces and applications ⋮ Some new fixed point theorems for \(\alpha\)-Geraghty contraction type maps in metric spaces ⋮ Fixed point theorems for \((\psi, \beta)\)-Geraghty contraction type maps in ordered metric spaces and some applications to integral and ordinary differential equations ⋮ Unnamed Item ⋮ Study of implicit relation in w-distance and (η,θ,Z,φ)β-contraction in wt-distance with an application ⋮ Fixed points of α-Θ-Geraghty type and Θ-Geraghty graphic type contractions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Common fixed point of \((\psi, \beta)\)-generalized contractive mappings in partially ordered metric spaces ⋮ Some applications with new admissibility contractions in b-metric spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Existence of solutions of integral equations via fixed point theorems ⋮ A note on `\(\psi\)-Geraghty type contractions' ⋮ Fuzzy fixed points of generalized F2-Geraghty type fuzzy mappings and complementary results ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Fixed point theorems for Geraghty-type mappings applied to solving nonlinear Volterra-Fredholm integral equations in modularG-metric spaces ⋮ \(\alpha\)-\(\psi\)-Geraghty contractions on generalized metric spaces

Cites Work

• Coupled coincidence point theorems for contractions without commutative condition in intuitionistic fuzzy normed spaces
• Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type
• Generalization of fixed point theorems in ordered metric spaces concerning generalized distance
• Coupled fixed point theorems for contractions in intuitionistic fuzzy normed spaces
• Coupled common fixed point theorems for \(w^{\ast }\)-compatible mappings in ordered cone metric spaces
• Coupled fixed points of weakly \(F\)-contractive mappings in topological spaces
• A generalization of Mizoguchi and Takahashi's theorem for single-valued mappings in partially ordered metric spaces
• Common fixed point theorems on generalized distance in ordered cone metric spaces
• Generalized weak contractions in partially ordered metric spaces
• Fixed points of Geraghty-type mappings in various generalized metric spaces
• Common fixed point theorems for \(c\)-distance in ordered cone metric spaces
• Fixed-point theorems in partially ordered metric spaces for operators with PPF dependence
• Fixed point theorems for weakly contractive mappings in partially ordered sets
• Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces
• Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces
• Some results on weakly contractive maps
• Fixed point theorems for generalized contractions in ordered metric spaces
• Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations
• Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations
• Fixed point theorems in partially ordered metric spaces and applications
• Common fixed point theorems for four mappings in TVS-Valued cone metric spaces
• Fixed point theorems in ordered abstract spaces
• THE EXISTENCE RESULTS OF COUPLED QUASI-SOLUTIONS FOR A CLASS OF OPERATOR EQUATIONS
• A fixed point theorem in partially ordered sets and some applications to matrix equations
• Generalized contractions in partially ordered metric spaces
• On Contractive Mappings
• Fixed point theorems in ordered 𝐿-spaces
• A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations

This page was built for publication: A generalization of Geraghty's theorem in partially ordered metric spaces and applications to ordinary differential equations