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Vector Equilibrium Problems with Generalized Monotone Bifunctions
AbstractA vector equilibrium problem is defined as follows: given a closed convex subset K of a real topological Hausdorff vector space and a bifunction F(x, y) valued in a real ordered locallyExpand
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From Scalar to Vector Equilibrium Problems in the Quasimonotone Case
In a unified approach, existence results for quasimonotone vector equilibrium problems and quasimonotone (multivalued) vector variational inequality problems are derived from an existence result forExpand
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On Quasimonotone Variational Inequalities
The purpose of this paper is to prove the existence of solutions of the Stampacchia variational inequality for a quasimonotone multivalued operator without any assumption on the existence of innerExpand
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Continuity and Maximality Properties of Pseudomonotone Operators
£is called pseudomonotone (in Karamardian’s sense) if for all (x;x £ ) and (y;y £ ) in its graph, hx £ ;y † xi µ 0 implies hy £ ;y † xi µ 0. We deflne an equivalence relation on the set ofExpand
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Quasimonotone variational inequalities in Banach spaces
Various existence results for variational inequalities in Banach spaces are derived, extending some recent results by Cottle and Yao. Generalized monotonicity as well as continuity assumptions on theExpand
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Characterization of Nonsmooth Semistrictly Quasiconvex and Strictly Quasiconvex Functions
New concepts of semistrict quasimonotonicity and strict quasimonotonicity for multivalued maps are introduced. It is shown that a locally Lipschitz map is (semi)strictly quasiconvex if and only ifExpand
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Handbook of Generalized Convexity and Generalized Monotonicity
The chapters are as follows: Introduction to Convex and Quasiconvex Analysis (J.B.G.Frenk, G. Kassay) Criteria for Generalized Convexity and Generalized Monotonicity in the Differentiable Case (J.-P.Expand
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Coercivity conditions and variational inequalities
TLDR
We show that in reflexive Banach spaces if the assumptions used for bounded domains hold, then various coercivity conditions introduced in the literature are equivalent to each other and that they are not only sufficient, but also necessary for the set of solutions to be non-empty and bounded. Expand
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On the Subdifferentials of Quasiconvex and Pseudoconvex Functions and Cyclic Monotonicity
Abstract The notions of cyclic quasimonotonicity and cyclic pseudomonotonicity are introduced. A classical result of convex analysis concerning the cyclic monotonicity of the (Fenchel–Moreau)Expand
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On strong pseudomonotonicity and (semi)strict quasimonotonicity
New concepts of strong pseudomonotonicity, strict quasimonotonicity, and semistrict quasimonotonicity of a map are introduced and their properties are studied. In the case of a differentiableExpand
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