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Controllers as fixed points of set-valued operators
Proceedings of Tenth International Symposium on Intelligent Control, 1995Considers the problem of constructing a "controller" for a hybrid system which will solve the viability problem that all points of plant trajectories stay inside a given "viability set". Here, a "controller" is a network of three successive devices, a digital to analog converter, a digital program (a computer together with its control software), and an
Anil Nerode +2 more
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Existence Theorems for Set-valued Operators in Banach Spaces
Set-Valued Analysis, 2006For a nonempty closed convex subset \(C\) of a real Banach space \(E\), let \(N_C(x)\) be the normal cone of \(C\) at \(x\in C\), that is, \(N_C(x)=\{ x^*\in E^*: \langle x-y, x^*\rangle \geq 0\), \(\forall y\in C\}\). The authors study the existence of points \(x\in X\) satisfying \(0\in Tx\), where \(T:X\rightarrow 2^{E^*}\) is a set-valued operator ...
Shin-ya Matsushita, Wataru Takahashi
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On Nemytskii operator for set-valued functions
Publicationes Mathematicae Debrecen, 1999The author presents generalizations (in some sense) of her previous results that appeared in [Publ. Math. 54, No. 1-2, 33-37 (1999; Zbl 0921.47056)]. In fact, here she treats the problem of characterizing those vector-valued, or set-valued functions that generate such a Nemytskij operator which maps a \(\text{lip}^2\) space (space of functions with ...
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On the Convergence of Discretizations for Set Valued Operator Equations
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1997AbstractThis paper is concerned with the theory of the convergence of discretizations for set‐valued operator equations. It is a continuation of investigations in [2], [7], [5], some results for one‐valued operators have been generalized herein. As an application, two examples for set‐valued differential equations are discussed.
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Set-valued nonlinear contractive operators in PM-spaces
2021In this paper, we consider some nonlinear contraction for set-valued operators and prove some fixed point results in the case of set-valued operators are ordered-close and not ordered-close, and in the case of set-valued operators are UCAV (LCAV) in quasi-ordered $PM$-spaces.
Lotfali Ghasab, Ehsan +3 more
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On Single-Valuedness of Quasimonotone Set-Valued Operators
2017A Nash problem is a noncooperative game in which the objective function of each player also depends on the decision variable of the other player. In order to solve such difficult problem, a classical approach is to write the optimality conditions of each of the problems obtaining thus a variational inequality.
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The generalized -projection operator and set-valued variational inequalities in Banach spaces
Nonlinear Analysis: Theory, Methods & Applications, 2009In [Bull. Aust. Math. Soc. 73, No. 2, 307--317 (2006; Zbl 1104.47053)], the authors introduced the following notion of generalized \(f\)-projection operator: Let \(B\) be a Banach space and \(B^{*}\) be its dual. Let \(K\) be a nonempty, closed and convex subset of \(B\).
Wu, Ke-Qing, Huang, Nan-Jing
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Linguistic set-valued decision making based on LWA operator
2010 IEEE International Conference on Industrial Engineering and Engineering Management, 2010In linguistic group decision analysis, we need to solve group decision making with uncertain linguistic information. By analyzing many illustrative example, we notice that not all of linguistic values of the initial linguistic expression domain are used to evaluate decision making problem.
Xuezheng Zhang, Qian Zhu, Zheng Pei
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A global bifurcation index for set-valued perturbations of Fredholm operators
Nonlinear Analysis: Theory, Methods & Applications, 2010Let \(E\) and \(F\) be Banach spaces. This paper is devoted to the study of the solvability and the behavior of solutions to parametrized equations and inclusions of the form \[ Lx\in \varphi (\lambda,x), \] where \(\lambda\) belongs to a parameter space \(\Lambda,\) \(x\in U\subset E,\) \(L:E\to F\) is a linear Fredholm operator of non-negative index ...
Gabor, Dorota, Kryszewski, Wojciech
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Proximal Methods for Variational Inequalities with Set-Valued Monotone Operators
2001A general approach to analyse convergence and rate of convergence of the proximal-like methods for variational inequalities with set-valued maximal monotone operators is developed. It is oriented to methods coupling successive approximation of the variational inequality with the proximal point algorithm as well as to related methods using ...
A. Kaplan, R. Tichatschke
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