In this paper, we introduce a new class of bilevel equilibrium problems with lower and upper bounds in locally convex Hausdorff topological vector spaces and establish some conditions for the existence of solutions to...
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In this paper, we introduce a new class of bilevel equilibrium problems with lower and upper bounds in locally convex Hausdorff topological vector spaces and establish some conditions for the existence of solutions to these problems using the Kakutani-Fan-Glicksberg fixed-point theorem. Then, we establish generic stability of set-valued mappings and we show the set of essential points of a map is a dense residual subset of a (Hausdorff) metric space of set-valued maps for bilevel equilibrium problems with lower and upper bounds. The results presented in the paper are new and extend the main results given by some authors in the literature. (C) 2019 Elsevier B.V. All rights reserved.
In this paper, we study a new kind of vector equilibrium problem and we proved the existence of solutions for this kind of equilibrium problem by using the section theorem and Fan KKM theorem. Then we generalize this ...
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In this paper, we study a new kind of vector equilibrium problem and we proved the existence of solutions for this kind of equilibrium problem by using the section theorem and Fan KKM theorem. Then we generalize this kind of vector equilibrium problem to a more general case. equilibrium problems with lower and upper bounds was an open problem proposed by Isac, Sehgal and Singh in 1999. ***, ***, *** and ***, Zhang Cong-jun derived some results of the equilibrium problems with lower and upper bounds under certain conditions. In this paper we derive more results of this open problem under certain conditions, constructs an iteration algorithm, and discuses the convergence of the algorithm. (c) 2006 Elsevier Ltd. All rights reserved.
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