Selections of Bounded Variation

DOI10.1515/JAA.2004.1zbMath1077.26015MaRDI QIDQ4659529

Vyacheslav V. Chistyakov

Publication date: 21 March 2005

Published in: Journal of Applied Analysis (Search for Journal in Brave)

zbMATH Keywords

set-valued mappingsselectionsgeneralized variationmultivalued superposition operators

Mathematics Subject Classification ID

Set-valued functions (26E25) Set-valued maps in general topology (54C60) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Selections in general topology (54C65) Functions of bounded variation, generalizations (26A45)

Related Items (34)

Uniformly bounded composition operators on the space of bounded variation functions in the sense of Waterman ⋮ Pointwise selection theorems for metric space valued bivariate functions ⋮ The approximate variation of univariate uniform space valued functions and pointwise selection principles ⋮ Selections of bounded variation under the excess restrictions ⋮ Selection principles for maps of several variables ⋮ Topologies and measures on the space of functions of bounded variation taking values in a Banach or metric space ⋮ On the smoothness of value functions and the existence of optimal strategies in diffusion models ⋮ A pointwise selection principle for maps of several variables via the total joint variation ⋮ The metric integral of set-valued functions ⋮ Selection properties and set-valued Young integrals of set-valued functions ⋮ A generalization of the Helly theorem for functions with values in a uniform space ⋮ Unnamed Item ⋮ A note on tameness of families having bounded variation ⋮ On metric semigroups-valued functions of bounded Riesz-\(\Phi\)-variation in several variables ⋮ A pointwise selection principle for metric semigroup valued functions ⋮ A selection principle for uniform space-valued functions ⋮ Fixed points of modular contractive maps ⋮ Locally Lipschitz composition operators in space of the functions of bounded \(\kappa \Phi\)-variation ⋮ A Banach algebra of functions of several variables of finite total variation and Lipschitzian superposition operators. I ⋮ Maps of several variables of finite total variation. II: E. Helly-type pointwise selection principles ⋮ Maps of several variables of finite total variation. I: Mixed differences and the total variation ⋮ Measure differential inclusions through selection principles in the space of regulated functions ⋮ Metric modulars and their application ⋮ Selection principle for pointwise bounded sequences of functions ⋮ Generalised Presic type operators in modular metric space and an application to integral equations of Caratheodory type functions ⋮ Asymmetric variations of multifunctions with application to functional inclusions ⋮ The optimal form of selection principles for functions of a real variable ⋮ Modular metric spaces. I: Basic concepts ⋮ Modular metric spaces. II: Application to superposition operators ⋮ Mappings of bounded variation with values in a metric space: Generalizations ⋮ On Nemytskij operator in the space of absolutely continuous set-valued functions ⋮ Fixed point theorems in complete modular metric spaces and an application to anti-periodic boundary value problems ⋮ Set-valued functions of bounded generalized variation and set-valued Young integrals ⋮ Meir-Keeler type contractions on modular metric spaces

Cites Work

• Continuous selections. I
• Continuity properties of selectors and Michael's theorem
• On some propertis of functions of generalized variation
• A measurable selection theorem for compact-valued maps
• Differentiable selections and Castaing representations of multifunctions
• On maps of bounded \(p\)-variation with \(p>1\)
• A selection principle for mappings of bounded variation
• Superposition operators in the algebra of functions of two variables with finite total variation
• Lipschitz retracts, selectors, and extensions
• \(L_ p\)-continuous extreme selectors of multifunctions with decomposable values: Existence theorems
• On mappings of bounded variation
• Mappings of bounded \(\Phi\)-variation with arbitrary function \(\Phi\)
• A continuous selection theorem for extremally disconnected spaces
• Lipschitzian Superposition Operators Between Spaces of Functions of Bounded Generalized Variation with Weight
• Selected Selection Theorems
• On a Characterization of Lipschitzian Operators of Substitution in the SpaceBV{a, b)
• A selection of convex-compact-valued multi-functions with remarkable properties: the steiner selection
• Survey of Measurable Selection Theorems
• On a theorem of E. Helly
• Lipschitzian composition operators in some function spaces
• Lipschitzian Operators of Substitution in the Algebra ΛBV
• On the extension and generation of set-valued mappings of bounded variation
• A fixed point theorem for set valued mappings
• Generalized variation of mappings with applications to composition operators and multifunctions

This page was built for publication: Selections of Bounded Variation