On uniformly continuous Nemytskij operators generated by set-valued functions [PDF]
Aequationes mathematicae, 2010 The properties of superposition operators generated by set-valued functions are studied. The main result is the following. Theorem. Let \(I = [0, 1]\) and \(Y\) be a real normed linear space, \(Z\) be a Banach space and let \(C\) be a convex cone in \(Y\). Assume that \(\gamma: [0, \infty) \rightarrow [0, \infty)\) is continuous at \(0\), \(\gamma(0) =
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IEEE Access, 2019 Considering decision makers (DMs) maybe hesitant among a set of values when determining the membership and non-membership degrees in a q-rung orthopair fuzzy environment, the q-rung dual hesitant fuzzy sets (q-RDHFS) were proposed.
Yuan Xu +5 more
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, the set of Lipschitz continuous operators is a set of first category in the set of uniformly continuous operators [PDF]
, 2019 International audienceIn this paper, we prove that the set of Lipschitz continuous nonlinear operators defined from ℒ 2 into ℒ 2 is dense on the set of uniformly continuous operators and is furthermore a set of first category in the same set.
Scorletti, Gérard +3 more
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Continuous dependence and fixed points for some multivalued operators
Journal of Numerical Analysis and Approximation Theory, 1997 In this paper we extend the notion of \(I^0\)-continuity and uniform \(I^0\)-continuity from [2] to set-valued operators. For families of such operators we prove (semi)continuity of the fixed point sets.
Eduard Kirr, Adrian Petrușel
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On the Representation of Hysteresis Operators Acting on Vector-Valued, Left-Continuous and Piecewise Monotaffine and Continuous functions [PDF]
, 2015 In Brokate-Sprekels 1996, it is shown that hysteresis operators acting on scalar-valued, continuous, piecewise monotone input functions can be represented by functionals acting on alternating strings.
Klein, Olaf
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Two Integral Operators Defined with Bessel Functions on the Class N(β) [PDF]
, 2013 Using Bessel functions of first kind we introduce new integral operators and show that these operators are in the class N(β)
Nicoleta Ularu
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Approximate Convexity of Set-Valued Mappings and Variational Inequalities
MathematicsIn this article, we introduce the notion of approximate convexity for set-valued mappings, specifically in the forms of approximate pseudoconvexity and approximate quasiconvexity.
Dalal Alhwikem
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On boundary value problems for degenerate differential inclusions in Banach spaces
Abstract and Applied Analysis, 2003 We consider the applications of the theory of condensing set-valued maps, the theory of set-valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive ...
Valeri Obukhovskii, Pietro Zecca
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Approximation Operators Based on L-Fuzzy Set-Valued Mappings [PDF]
Proceedings on Intelligent Systems and Knowledge Engineering (ISKE2007), 2007 In this paper, the fuzziness of Gomolinska approximation space based on uncertainty mappings was introduced. It is proved that many approximation operators could be constructed by composition of basic approximation operators.
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Point-based set-valued approximation, C-differentiable operator and application [PDF]
, 2003 In this article, we investigate the point-based set-valued approximation [H. Xu (1999). Set-valued approximation and Newton's methods. Mathematical Programming, 84, 401-420.] and the C-differential operator [L. Qi (1996).
Xu, Huifu
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