Results 171 to 180 of about 49,937 (203)

The generalized -projection operator and set-valued variational inequalities in Banach spaces

Nonlinear Analysis: Theory, Methods & Applications, 2009
In [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, 2010
In 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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On Single-Valuedness of Quasimonotone Set-Valued Operators

2017
A 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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A global bifurcation index for set-valued perturbations of Fredholm operators

Nonlinear Analysis: Theory, Methods & Applications, 2010
Let \(E\) 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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General -monotone operators and perturbed iterations for nonlinear set-valued relaxed cocoercive operator inclusion problems

Applied Mathematics and Computation, 2009
The article deals with some inclusion problems including general \(A\)-monotone operators \(M\). Let \({\mathcal B}\) be a Banach space with dual space \({\mathcal B}^*\), \(A: \;{\mathcal B} \to {\mathcal B}^*\) be a linear or nonlinear operator; a set-valued operator \(M: \;{\mathcal B} \to 2^{\mathcal B}\) is called (by the authors) general \(A ...
Heng-you Lan, Le-Cai Cai, Zi-Shan Liu
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Set-valued extension of operators via Steiner selections (I)—Theoretical results

Applied Mathematics and Mechanics, 2002
A way to extend operators in spaces of continuous functions to spaces of continuous set-valued functions is obtained by the authors. This extension is developed through the Steiner selections of set-valued functions. Properties and characteristics of the convergence of sequences of operators of this class are studied.
Terán, Pedro, López-Dían, Miguel
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Proximal Methods for Variational Inequalities with Set-Valued Monotone Operators

2001
A 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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Averaging operators and set-valued maps

2016
We investigate maps admitting, in general, non-linear averaging operators. Characterizations of maps admitting a normed, weakly additive averaging operator which preserves max (resp., min) and weakly preserves min (resp., max) is obtained. We also describe set-valued maps into completely metrizable spaces admitting lower semi-continuous selections.
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On Nemytskij operator in the space of absolutely continuous set-valued functions

Journal of Applied Analysis, 2011
Summary: We consider the Nemytskij operator, defined by \((N\phi)(x) := G(x, \phi(x))\), where \(G\) is a given set-valued function. It is shown that if \(N\) maps \(AC(I, C)\), the space of all absolutely continuous functions on the interval \(I := [0, 1]\) with values in a cone \(C\) in a reflexive Banach space, into \(AC(I, \mathcal K)\), the space ...
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Monotone operators in stochastic set-valued equations

Nonlinear Analysis: Theory, Methods & Applications, 2001
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