Fixed Points and Stationary Points of Dissipative Multivalued Maps

DOI10.2307/2042331zbMath0446.47049OpenAlexW4238177300MaRDI QIDQ3891278

Jean-Pierre Aubin, Jerrold Siegel

Publication date: 1980

Full work available at URL: https://doi.org/10.2307/2042331

zbMATH Keywords

entropymultivalued mapscontraction theorem

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Fixed-point theorems (47H10)

Related Items (67)

Hausdorff quasi-distances, periodic and fixed points for Nadler type set-valued contractions in quasi-gauge spaces ⋮ Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings ⋮ Fuzzy quasi-triangular spaces, fuzzy sets of Pompeiu-Hausdorff type, and another extensions of Banach and Nadler theorems ⋮ Endpoints of multivalued nonexpansive mappings in geodesic spaces ⋮ On stationary points of nonexpansive set-valued mappings ⋮ An inertial projection and contraction method with a line search technique for variational inequality and fixed point problems ⋮ Strict equilibria of multi-valued maps and common fixed points ⋮ Unnamed Item ⋮ Endpoints of set-valued dynamical systems of asymptotic contractions of Meir-Keeler type and strict contractions in uniform spaces ⋮ Cone uniform, cone locally convex and cone metric spaces, endpoints, set-valued dynamic systems and quasi-asymptotic contractions ⋮ Ekeland's variational principle and minimization Takahashi's theorem in generalized metric spaces ⋮ Dynamic processes, fixed points, endpoints, asymmetric structures, and investigations related to Caristi, Nadler, and Banach in uniform spaces ⋮ Nadler's type principle with high order of convergence ⋮ The uniqueness of endpoints for set-valued dynamical systems of contractions of Meir-Keeler type in uniform spaces ⋮ Ekeland's variational principle, minimax theorems and existence of nonconvex equilibria in complete metric spaces ⋮ Existence and uniqueness of endpoints of closed set-valued asymptotic contractions in metric spaces ⋮ Fixed point theorems for multivalued maps in cone metric spaces ⋮ Fixed point and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces ⋮ Poincaré's recurrence theorems for set-valued dynamical systems ⋮ Quasi-triangular spaces, Pompeiu-Hausdorff quasi-distances, and periodic and fixed point theorems of Banach and Nadler types ⋮ Generalized uniform spaces, uniformly locally contractive set-valued dynamic systems and fixed points ⋮ The drop theorem, the petal theorem and Ekeland's variational principle ⋮ Some equivalent formulations of the generalized Ekeland's variational principle and their applications ⋮ Fixed point theorems for multivalued contractive mappings and multivalued Caristi type mappings in cone metric spaces ⋮ Vectorial form of Ekeland-type variational principle ⋮ Fixed points and endpoints of contractive set-valued maps in cone uniform spaces with generalized pseudodistances ⋮ Stationary points of lower semicontinuous multifunctions ⋮ Set-valued Leader type contractions, periodic point and endpoint theorems, quasi-triangular spaces, Bellman and Volterra equations ⋮ Endpoints of set-valued asymptotic contractions in metric spaces ⋮ Fixed point theorems of mean nonexpansive set-valued mappings in Banach spaces ⋮ Quasigauge spaces with generalized quasipseudodistances and periodic points of dissipative set-valued dynamic systems ⋮ Common stationary point of multivalued asymptotically regular mappings ⋮ Endpoints of multi-valued generalized weak contraction mappings ⋮ Equivalent formulations of Ekeland's variational principle ⋮ Monotone viable trajectories for functional differential inclusions ⋮ Approximate endpoints for set-valued contractions in metric spaces ⋮ Mean value theorems via maximal element techniques ⋮ Endpoints of multivalued contraction operators ⋮ Generalized contractions of Meir-Keeler type, endpoints, set-valued dynamical systems and generalized pseudometrics in uniform spaces ⋮ Endpoint theory for set-valued nonlinear asymptotic contractions with respect to generalized pseudodistances in uniform spaces ⋮ Approximating stationary points of multivalued generalized nonexpansive mappings in metric spaces ⋮ Periodic point, endpoint, and convergence theorems for dissipative set-valued dynamic systems with generalized pseudodistances in cone uniform and uniform spaces ⋮ Equivalent extensions to Caristi-Kirk's fixed point theorem, Ekeland's variational principle, and Takahashi's minimization theorem ⋮ Gregus-type common fixed point theorems for tangential multivalued mappings of integral type in metric spaces ⋮ Set-valued dynamic systems and random iterations of set-valued weaker contractions in uniform spaces ⋮ Ekeland's variational principle for vectorial multivalued mappings in a uniform space ⋮ Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudodistances ⋮ Fixed points of dynamic processes of set-valued \(F\)-contractions and application to functional equations ⋮ Some asymptotic stationary point theorems in topological spaces ⋮ Convergence of dissipative-like dynamics and algorithms governed by set-valued nonexpansive mappings ⋮ Local completeness, Pareto efficiency and Mackey Bishop-Phelps cones ⋮ Approximating endpoints of multi-valued nonexpansive mappings in Banach spaces ⋮ Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces ⋮ Nonconvex minimization problems ⋮ Drop theorems and lipschitzianness tests via maximality procedures ⋮ Quasi-asymptotic contractions, set-valued dynamical systems, uniqueness of endpoints and generalized pseudodistances in uniform spaces ⋮ Fixed points for non-self operators and domain invariance theorems ⋮ Common fixed points for multivalued generalized contractions on partial metric spaces ⋮ Fixed point theory for a new type of contractive multivalued operators ⋮ Iterative approximation of endpoints for multivalued mappings in Banach spaces ⋮ Unnamed Item ⋮ Some fixed point theorems for fuzzy mappings ⋮ Set-valued \(\alpha\)-almost convex mappings ⋮ Multivalued mappings ⋮ Convergence theorems, best approximation and best proximity for set-valued dynamic systems of relatively quasi-asymptotic contractions in cone uniform spaces ⋮ Endpoints of set-valued contractions in metric spaces ⋮ Differential Lipschitzianness tests on abstract quasi-metric spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the variational principle
• Dissipative dynamical systems. II: Linear systems with quadratic supply rates
• Fixed Point Theorems for Mappings Satisfying Inwardness Conditions
• A New Proof of Caristi's Fixed Point Theorem
• Convergence Conditions for Nonlinear Programming Algorithms

This page was built for publication: Fixed Points and Stationary Points of Dissipative Multivalued Maps