New results in the theory of multivalued mappings. I: Topological characteristics and solvability of operator relations

DOI10.1007/BF02207025zbMath0711.55002OpenAlexW2018383913MaRDI QIDQ923419

Yu. G. Borisovich, A. D. Myshkis, Valerii V. Obukhovskij, Boris Danilovich Gel'man

Publication date: 1990

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02207025

zbMATH Keywords

multivalued mappingsfixed pointdegreecoincidence

Mathematics Subject Classification ID

Degree, winding number (55M25) Fixed points and coincidences in algebraic topology (55M20)

Related Items

Cascade search principle and its applications to the coincidence problems of \(n\) one-valued or multi-valued mappings

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• Non-linear eigenvalue problems and bifurcations for differentiable multivalued maps
• ON SOLUTIONS OF A DIFFERENTIAL INCLUSION WITH LOWER SEMICONTINUOUS NONCONVEX RIGHT-HAND SIDE IN A BANACH SPACE
• Semistability of motions and regular dependence of limit sets on points in general semi-sytems
• Almost-periodic forcing for a wave equation with a nonlinear, local damping term
• $c$-continuity and closed graphs
• Selectors for Borel Sets with Large Sections
• Über implizite Inklusionen und Bifurkation
• Multivalued solutions of a linear functional equation
• Existence of Value in Generalized Pursuit-Evasion Games
• An Analytic Set-Valued Selection and Its Applications to the Corona Theorem, to Polynomial Hulls and Joint Spectra
• On Semigroups Generated by m-Accretive Operators in a Strict Sense
• Abstract Nonlinear Volterra Equations with Positive Kernels
• Existence of measurable selectors and parametrizations for $G_δ$-valued multifunctions
• Flow invariance and viability for differential inclusions
• FIXED POINT THEOREM FOR MULTIFUNCTIONS
• On the Convergence of a One-step Method for the Numerical Solution of an Ordinary Differential Inclusion
• The Value Function in Optimal Control: Sensitivity, Controllability, and Time-Optimality
• Continuity in semidynamical systems
• Coincidence Theorems for Hybrid Contractions
• Differentiation of Real-Valued Functions and Continuity of Metric Projections
• Multivalued contraction with parameter
• Representation of Set Valued Operators
• Fixed points of weakly inward multis
• Approximate Selections and Fixed Points for Upper Semicontinuous Maps with Decomposable Values
• Random Fixed Point Theorems for Measurable Multifunctions in Banach Spaces
• Fixed points of weakly inward multivalued maps
• On Random Approximations and a Random Fixed Point Theorem for Set Valued Mappings
• A minimum theorem for n-valued multifunctions
• Controllability and feedback systems
• Asymptotic behaviour of the solutions of second order difference equations associated to monotone operators
• Nonsmooth Analysis: Differential Calculus of Nondifferentiable Mappings
• Sur une certaine alternative non-linéaire en analyse convexe
• Multivalued contractions and applications to functional differential equations
• Open and Proper Maps Characterized by Continuous Setvalued Maps
• Functional differential equations in Banach spaces: Growth and decay of solutions.
• Metric projections and the differentiability of distance functions
• Hyperspaces of H-Closed Spaces
• On conditions warranting Φ-subdifferentiability
• Description of a class of multivalued differential equations with almost weakly stable trivial solution
• Some continuity properties of polyhedral multifunctions
• Stability of solutions of nonlinear boundary-value problems for hyperbolic systems
• Set-valued perturbations of differential equations at resonance
• Continuous selections and countable sets
• On fixed points and variational inequalities—a circular tour
• Some remarks on set-valued dynamical systems
• On measurable relation
• Higher order differentiability of multifunctions
• On nonlinear parabolic equations with abruptly changing nonlinear boundary conditions
• Conditions for the Uniqueness of the Fixed Point in Kakutani's Theorem
• On the attainable set at time T for multivalued differential equations
• Existence for a nonlinear hyperbolic system
• An Application of Glicksberg’s Theorem to Set-Valued Integral Equations Arising in the Theory of Thermostats
• A characterization of tangential regularity
• Multivalued mappings and Filippov's operation
• Some fixed point and almost fixed point theorems for multivalued mappings in topological vector spaces
• Applications of the u-Closure Operator
• A Fixed Point Theory for Multi-Valued Mappings
• Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems
• On the solvability of x∈Tx+λFx in quasinormal cones with T and F k-set-contractive
• Periodic solutions to differential inclusions
• Implicit Degenerate Evolution Equations and Applications
• Topological degree methods in multi-valued boundary value problems
• Invariant sets for functional differential equations in Banach spaces and applications
• Estimates on the support of the solutions of some nonlinear elliptic and parabolic problems
• Banach-Steinhaus Theorem for Multivalued Mappings
• A fixed point interpretation of Pareto optimization
• On the Maximality of the Sum of Monotone Operators
• On nonparasit generalized solutions of differential relations
• Sets of solutions of differential relations
• Theory of Fréchet cones
• A characterization of pointwise-lipschitz-continuous selections for the metric projection
• Global and point controllability of uncertain dynamical systems
• ON THE CONVERGENCE OF THE SEQUENCE OF OPTIMAL STRATEGIES FOR A CERTAIN FUNCTIONAL EQUATION OF THE DYNAMIC PROGRAMMING
• On Abstract Quasi Variational Inequalities. Approximation of Solutions. I
• Nonzero solutions of nonlinear systems of differential equations via fixed point theorems for multivalued maps
• Characterization of Continuous Selections of the Metric Projection for a Class of Weak Chebyshev Spaces
• On generalized differentials and subdifferentials of Lipschitz vector-valued functions
• Fixed Points of Subopen Multifunctions
• An existence result for a class of nonlinear evolution equations in Banach spaces
• The modulus of coninuity of the set-valued metric projection
• Topological properties of the sets of solutions for functional differential inclusions
• Comparison Theorems on Minimax Inequalities, Variational Inequalities, and Fixed Point Theorems
• The fixed point property for set-valued mappings
• Compact Perturbations of m-Accretive Operators in General Banach Spaces
• On the Convergence of Closed-Valued Measurables Multifunctions
• Solution periodique d'une équation d'évolution
• Some remarks on set-valued mappings
• Some Remarks on the Convergence of Approximate Solutions of Nonlinear Evolution Equations in Hilbert Spaces
• One-to one Carathéodory representation theorem for multifunctions with uncountable values
• Recurrence set-relations in stochastic multiobjective dynamic decision processes
• Dissipativity in the sense of Levinson for a class of second—order nonlinear evolution equations
• Asymptotic behaviour of some second order evolution equations
• Minimax theorems for upper semicontinuous functions
• Fixed Points of Nonexpansive Condensing Multi-Valued Mappings on Metric Spaces
• Distribution des valeurs des fonctions analytiques multiformes
• Remarks on nonlinear functional equations
• Theorems of Namioka and R. E. Johnson Type for Upper Semicontinuous and Compact Valued Set-Valued Mappings
• On the asymptotic behaviour of solutions of volterra equations in Hilbert space
• The Role of Countable Dimensionality in the Theory of Cell-Like Relations
• Uniqueness of the maximal extension of a monotone operator
• Singular Perturbation in Mayer’s Problem for Linear Systems
• Locally Contractive and Expansive Mapping
• Hereditarily-Additive Families in Descriptive Set Theory and Borel Measurable Multimaps
• Hyperspaces of quotient and subspaces I. Hausdorff topological spaces
• General network equilibrium analysis
• Surjectivity of φ-Accretive Operators
• GENERALIZED FIXED POINT THEOREM
• A sufficient condition for lower semicontinuity of solution sets of systems of convex inequalities
• On continuity and compactness of some nonlinear operators associated with differential equations in noncompact intervals
• Application of a Selection Theorem to Hyperspace Contractibility
• Continuous Selections for Weakly Hausdorff Lower Semicontinuous Multifunctions
• Parametrizations of Borel Sets with Large Sections
• Averaged Multivalued Solutions for Scalar Conservation Laws
• Measurable selectors of \underline{𝑃𝐶𝐴} multifunctions with applications
• Generalized equations: Solvability and regularity
• Komplementaritätsprobleme für punkt-menge-abbildungen
• Generic Frechet Differentiability of Convex Operators
• Certain geometric properties of covariant functors
• [https://portal.mardi4nfdi.de/wiki/Publication:3689923 La multi-application m�dianes conditionnelles]
• Measurable One-to-One Selections and Transition Kernels
• A representation theorem for compact-valued multifunctions
• Lipschitzian properties of multifunctions
• Convergence of Viable Solutions of Differential Inclusions with Convex Compact Graphs
• SOME FIXED POINTS THEOREMS FOR MULTI-VALUED MAPPINGS
• On the search for Borel $1$ selections
• On the Range of Maximal Monotone Operators in Nonreflexive Spaces
• Subopen multifunctions and selections
• Cyclical monotonicity of maximal monotone step operators
• Trajectories of set valued integrals
• Multi-valued solutions of a functional equation
• Existence of solutions of functional-differential inclusion in nonconvex case
• SOME COMMON FIXED POINT THEOREMS FOR MULTI-VALUED MAPPINGS
• A coincidence theorem in topological vector spaces
• On the asymptotic behavior of solutions of evolution equations associated with nonlinear Volterra equations
• Existence of Overtaking Optimal Trajectories for Problems with Convex Integrands
• Convergence of Conditional Expectations and Strong Laws of Large Numbers for Multivalued Random Variables
• On the tangency of multifunctions
• On De Blasi's differentiation theory for multifunctions
• Many-valued absolute retracts and absolute extensors in dimensions 0 and 1
• Continuous selections for a class of non-convex multivalued maps
• Interpolation and Extrapolation of Analytic Multivalued Functions
• Set mappings of unrestricted order
• Bounds for the set of solutions of functional-differential equations
• Fix-finite approximation of n-valued multifunctions
• On convergence of successive approximations of some generalized contraction mappings
• Directional contractors and fixed points of multivalued mappings
• Single-Valued Representation of Set-Valued Mappings II; Application to Differential Inclusions
• Calculus of Dini subdifferentials of functions and contingent coderivatives of set-valued maps
• Gradient Method for Nondensely Defined Closed Unbounded Linear Operators
• Coincidence theorems, minimax theorems, and variational inequalities
• Generalized functional-differential equations of neutral type
• Positive solutions of operator equations in the nondifferentiable case
• An index and a Nielsen number for n-valued multifunctions
• A variational method for nonlinear multivalued operators
• An extension of the essential supremum concept with applications to normal integrands and multifunctions
• Some applications of fixed point theorems for multivalued mappings on minimax problems in topological vector spaces
• Topological degree and Sperner's lemma
• Fixed point sets of continuum-values mappings
• Stability property of a class of variational inequalities
• Fixed-point theorems for set-valued mappings and existence of best approximants
• Classical hierarchies from a modern standpoint. Part I. C-sets
• Complete Closedness of Maximal Monotone Operators
• Evolutions governed by m-accretive plus compact operators
• A survey of metric selections
• Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections
• Surjectivity of multifunctions under generalized differentiability assumptions
• Leray-Schauder type continuation theorems for some nonlinear equations in Banach spaces
• Some remarks on nonlinear functional equations
• Global Behavior of Generalized Equations: A Sard Theorem
• Continuity of solutions of a singular parabolic equation
• A Degree for Operators of Monotone Type
• On regularization of right hand sides of differential relations
• Optimality Conditions for Distributed Control Problems with Nonlinear State Equation
• Fixed point index for open sets in euclidean spaces
• Contractors and fixed points
• A coincidence theorem for topological vector spaces
• A coincidence theorem for topological vector spaces
• Multivalued quasi-martingales and uniform amarts
• Fixed point theorems for fuzzy mappings
• Fuzzy random variables
• On nonlinear hyperbolic evolution equations with unilateral conditions dependent on time
• Set-valued mappings on metric spaces