Generalized distance and existence theorems in complete metric spaces
From MaRDI portal
Publication:5927578
DOI10.1006/jmaa.2000.7151zbMath0983.54034OpenAlexW1981163701MaRDI QIDQ5927578
Publication date: 23 April 2002
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jmaa.2000.7151
\(\tau\)-distance\(w\)-distanceBanach contraction principleCaristi's fixed point principleTataru's distance
Set-valued and variational analysis (49J53) Complete metric spaces (54E50) Fixed-point and coincidence theorems (topological aspects) (54H25)
Related Items (95)
Hausdorff quasi-distances, periodic and fixed points for Nadler type set-valued contractions in quasi-gauge spaces ⋮ Existence of fixed points for \(\Theta\)-type contraction and \(\theta\)-type Suzuki contraction in complete metric spaces ⋮ Some periodic and fixed point theorems on quasi-\(b\)-gauge spaces ⋮ Fixed point and periodic point results for \(\alpha\)-type \(F\)-contractions in modular metric spaces ⋮ A new type of Kannan's fixed point theorem in strong \(b\)-metric spaces ⋮ Fixed point theorems for Ćirić type mapping and application to integral equation ⋮ Fixed points of conditionally \(F\)-contractions in complete metric-like spaces ⋮ Fixed point theorems for F- contraction mapping in complete rectangular M-metric space ⋮ Coincidence Best Proximity Point Results via $$ w_{p}$$-Distance with Applications ⋮ Dynamic processes, fixed points, endpoints, asymmetric structures, and investigations related to Caristi, Nadler, and Banach in uniform spaces ⋮ Characterizations of reflexivity and compactness via the strong Ekeland variational principle ⋮ Generalizations of the strong Ekeland variational principle with a generalized distance in complete metric spaces ⋮ Ekeland-Type Variational Principles and Equilibrium Problems ⋮ Ekeland's variational principle, minimax theorems and existence of nonconvex equilibria in complete metric spaces ⋮ A definitive result on asymptotic contractions ⋮ Redefinition of \(\tau\)-distance in metric spaces ⋮ Kannan-type contractions and fixed points in uniform spaces ⋮ Some fixed point theorems for contractive multi-valued mappings induced by generalized distance in metric spaces ⋮ A generalization of Ekeland's variational principle by using the \(\tau\)-distance with its applications ⋮ Generalization of fixed point theorems in ordered metric spaces concerning generalized distance ⋮ A revised pre-order principle and set-valued Ekeland variational principles with generalized distances ⋮ Quasi-triangular spaces, Pompeiu-Hausdorff quasi-distances, and periodic and fixed point theorems of Banach and Nadler types ⋮ Fixed point results in quasi-cone metric spaces ⋮ Some fixed point theorems concerning \(F\)-contraction in complete metric spaces ⋮ Fixed point results for multivalued contractive maps ⋮ Generalized uniform spaces, uniformly locally contractive set-valued dynamic systems and fixed points ⋮ A fixed point theorem for generalized contractive type set-valued mappings with application to nonlinear fractional differential inclusions ⋮ An extension of Lakzian-Rhoades results in the structure of ordered b-metric spaces via \(wt\)-distance with an application ⋮ Fixed point theorems for generalized contractive type multivalued maps ⋮ Jachymski-Matkowski-Świątkowski's fixed point theorem ⋮ Fixed point theorems in ordered metric spaces via \(w\)-distances ⋮ Fixed points and endpoints of contractive set-valued maps in cone uniform spaces with generalized pseudodistances ⋮ Set-valued Leader type contractions, periodic point and endpoint theorems, quasi-triangular spaces, Bellman and Volterra equations ⋮ \(f\)-contractive multivalued maps and coincidence points ⋮ The weakest contractive conditions for Edelstein's mappings to have a fixed point in complete metric spaces ⋮ Unnamed Item ⋮ New completeness and periodic points of discontinuous contractions of Banach-type in quasi-gauge spaces without Hausdorff property ⋮ New generalized pseudodistance and coincidence point theorem in a \(b\)-metric space ⋮ Fixed point theorems and periodic problems for nonlinear Hill's equation ⋮ A fixed point theorem of Subrahmanyam type in uniform spaces with generalized pseudodistances ⋮ On Caristi-type mappings without lower semicontinuity assumptions ⋮ On generalized Ekeland's variational principle and equivalent formulations for set-valued mappings ⋮ On Ekeland's variational principle for Pareto minima of set-valued mappings ⋮ Fixed points and completeness in metric and generalized metric spaces ⋮ On Downing-Kirk's theorem. ⋮ Existence theorems for generalized distance on complete metric spaces ⋮ A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point ⋮ Remarks on ultrametrics and metric-preserving functions ⋮ Meir-Keeler contractions of integral type are still Meir-Keeler contractions ⋮ Set-valued fixed-point theorems for generalized contractive mappings without the Hausdorff metric ⋮ Two new types of fixed point theorems in complete metric spaces ⋮ Contractivity of leader type and fixed points in uniform spaces with generalized pseudodistances ⋮ New existence results for fixed point problem and minimization problem in compact metric spaces ⋮ Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory ⋮ Contractions of Banach, Tarafdar, Meir-Keeler, Ćirić-Jachymski-Matkowski and Suzuki types and fixed points in uniform spaces with generalized pseudodistances ⋮ Infinitely many solutions of \(p\)-Laplacian equations with limit subcritical growth ⋮ Functional variational principles and coercivity over normed spaces ⋮ On some nonlinear problems induced by an abstract maximal element principle ⋮ Caristi's fixed point theorem in semimetric spaces ⋮ Three fixed point theorems for generalized contractions with constants in complete metric spaces ⋮ Characterization of \(\Sigma\)-semicompleteness via Caristi's fixed point theorem in semimetric spaces ⋮ On maximal element theorems, variants of Ekeland's variational principle and their applications ⋮ Asymmetric structures, discontinuous contractions and iterative approximation of fixed and periodic points ⋮ On the relation between the weak Palais-Smale condition and coercivity given by Zhong ⋮ Convergence of the sequence of successive approximations to a fixed point ⋮ Equivalent extensions to Caristi-Kirk's fixed point theorem, Ekeland's variational principle, and Takahashi's minimization theorem ⋮ Systems of equilibrium problems with applications to new variants of Ekeland's variational principle, fixed point theorems and parametric optimization problems ⋮ Extensions and applications of ACF mappings ⋮ Generalized Caristi's fixed point theorems by Bae and others ⋮ Best proximity point theorems with Suzuki distances ⋮ The strong Ekeland variational principle ⋮ Function variational principles and coercivity ⋮ On Caristi type maps and generalized distances with applications ⋮ Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudodistances ⋮ Critical point theorems for nonlinear dynamical systems and their applications ⋮ The existence of fixed point theorems via \(w\)-distance and \(\alpha\)-admissible mappings and applications ⋮ On best proximity points for set-valued contractions of Nadler type with respect to \(b\)-generalized pseudodistances in \(b\)-metric spaces ⋮ Fixed point theorems for Kannan-type maps ⋮ Leader type contractions, periodic and fixed points and new completivity in quasi-gauge spaces with generalized quasi-pseudodistances ⋮ Brezis-Browder Principles and Applications ⋮ A generalized distance and enhanced Ekeland's variational principle for vector functions ⋮ Maximal and Variational Principles in Vector Spaces ⋮ A generalized Banach contraction principle that characterizes metric completeness ⋮ A new type of fixed point theorem in metric spaces ⋮ Minimax Theorems with Bregman Distance in Banach Spaces ⋮ Periodic and fixed points for Caristi-type \(G\)-contractions in extended \(b\)-gauge spaces ⋮ Fixed points for \(w\)-contractive multimaps ⋮ Subrahmanyam's fixed point theorem ⋮ Fixed points of multivalued maps in modular function spaces ⋮ Generalized Caristi's fixed point theorems ⋮ Variational principles with generalized distances and the modelization of organizational change ⋮ Some generalizations of fixed point theorems of Caristi type and Mizoguchi-Takahashi type under relaxed conditions ⋮ Multivalued SK-contractions with respect to \(b\)-generalized pseudodistances ⋮ A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point. II ⋮ A generalization of the Banach contraction principle in noncomplete metric spaces
Cites Work
- Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms
- Caristi's fixed point theorem and selections of set-valued contractions
- On Ekeland's variational principle and a minimax theorem
- Fixed point theorems and characterizations of metric completeness
- Nonconvex minimization problems
- Fixed Point Theorems for Mappings Satisfying Inwardness Conditions
- Contractive mappings, Kannan mappings and metric completeness
- Perturbed optimization on product spaces
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Generalized distance and existence theorems in complete metric spaces