Set-Valued Chaos in Linear Dynamics
Sign Up to like & getrecommendations! Published in 2017 at "Integral Equations and Operator Theory"
DOI: 10.1007/s00020-017-2394-6
Abstract: We study several notions of chaos for hyperspace dynamics associated to continuous linear operators. More precisely, we consider a continuous linear operator $$T : X \rightarrow X$$T:X→X on a topological vector space X, and the… read more here.
Keywords: space; chaos linear; set valued; valued chaos ... See more keywords
On Weakly Commuting Set-Valued Mappings on a Domain of Sets Endowed with Directed Graph
Sign Up to like & getrecommendations! Published in 2017 at "Results in Mathematics"
DOI: 10.1007/s00025-016-0588-x
Abstract: The aim of this paper is to present coincidence and common fixed point results of set-valued mappings satisfying certain generalized graphic F-contractive conditions on a family of sets endowed with a graph. It is worth… read more here.
Keywords: commuting set; valued mappings; weakly commuting; sets endowed ... See more keywords
Ohlin-Type Theorem for Convex Set-Valued Maps
Sign Up to like & getrecommendations! Published in 2020 at "Results in Mathematics"
DOI: 10.1007/s00025-020-01292-3
Abstract: A counterpart of the Ohlin theorem for convex set-valued maps is proved. An application of this result to obtain some inclusions related to convex set-valued maps in an alternative unified way is presented. In particular… read more here.
Keywords: valued maps; set valued; theorem convex; convex set ... See more keywords
Multi-utility representations of incomplete preferences induced by set-valued risk measures
Sign Up to like & getrecommendations! Published in 2020 at "Finance and Stochastics"
DOI: 10.1007/s00780-020-00440-5
Abstract: We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have to deal with multi-utility representations. We look for representations that… read more here.
Keywords: induced set; risk; valued risk; set valued ... See more keywords
Nonlinear expectations of random sets
Sign Up to like & getrecommendations! Published in 2019 at "Finance and Stochastics"
DOI: 10.1007/s00780-020-00442-3
Abstract: Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear… read more here.
Keywords: random sets; nonlinear expectations; set valued; finance ... See more keywords
An equilibrium version of set-valued Ekeland variational principle and its applications to set-valued vector equilibrium problems
Sign Up to like & getrecommendations! Published in 2017 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-016-6184-x
Abstract: By using Gerstewitz functions, we establish a new equilibrium version of Ekeland variational principle, which improves the related results by weakening both the lower boundedness and the lower semi-continuity of the objective bimaps. Applying the… read more here.
Keywords: version; equilibrium; set valued; vector equilibrium ... See more keywords
On Set Containment Characterizations for Sets Described by Set-Valued Maps with Applications
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Optimization Theory and Applications"
DOI: 10.1007/s10957-019-01605-9
Abstract: In this paper, dual characterizations of the containment of two sets involving convex set-valued maps are investigated. These results are expressed in terms of the epigraph of a conjugate function of infima associated with corresponding… read more here.
Keywords: containment characterizations; set containment; characterizations sets; valued maps ... See more keywords
Existence Results for Mixed Equilibrium Problems Involving Set-Valued Operators with Applications to Quasi-Hemivariational Inequalities
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Optimization Theory and Applications"
DOI: 10.1007/s10957-019-01629-1
Abstract: In this paper, we study the existence of solutions for mixed equilibrium problems associated with a set-valued operator in the general setting of vector spaces in duality, and in particular in Banach spaces. We use… read more here.
Keywords: quasi hemivariational; existence; mixed equilibrium; set valued ... See more keywords
Sensitivity analysis for set-valued equilibrium problems
Sign Up to like & getrecommendations! Published in 2020 at "Positivity"
DOI: 10.1007/s11117-020-00748-8
Abstract: In the paper, we mention a parametrized vector equilibrium problem via sum of two given set-valued maps, considered as a unified model of some problems in variational analysis and optimization. Then, we study sensitivity analysis… read more here.
Keywords: analysis; valued equilibrium; set valued; sensitivity analysis ... See more keywords
The Metric Integral of Set-Valued Functions
Sign Up to like & getrecommendations! Published in 2018 at "Set-Valued and Variational Analysis"
DOI: 10.1007/s11228-017-0403-1
Abstract: This paper introduces a new integral of univariate set-valued functions of bounded variation with compact images in ℝd${\mathbb {R}}^d$. The new integral, termed the metric integral, is defined using metric linear combinations of sets and… read more here.
Keywords: integral set; metric integral; valued functions; set valued ... See more keywords
Stability of metric regularity with set-valued perturbations and application to Newton’s method for solving generalized equations
Sign Up to like & getrecommendations! Published in 2017 at "Set-Valued and Variational Analysis"
DOI: 10.1007/s11228-017-0438-3
Abstract: In this paper, we deal firstly with the question of the stability of the metric regularity under set-valued perturbation. By adopting the measure of closeness between two multifunctions, we establish some stability results on the… read more here.
Keywords: stability metric; regularity set; metric regularity; set valued ... See more keywords