Very recently, a notion of cone b-metric was introduced as a generalization of b-metric, and some related fixed point results were obtained. In this paper, we investigate the answer to the question whether the given r...
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Very recently, a notion of cone b-metric was introduced as a generalization of b-metric, and some related fixed point results were obtained. In this paper, we investigate the answer to the question whether the given results generalize the existing ones or are equivalent to them.
In this paper, new nonlinear scalarization functions, which are different from the Gerstewitz function, are introduced. Some properties of these functions are discussed, and are used to prove new results on the existe...
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In this paper, new nonlinear scalarization functions, which are different from the Gerstewitz function, are introduced. Some properties of these functions are discussed, and are used to prove new results on the existence of solutions of generalized vector quasi-equilibrium problems with moving cones and the lower semicontinuity of solution mappings of parametric vector quasi-equilibrium problems. Detailed comparisons between our results and those obtained by using the Gerstewitz function (for existence theorems) and by other approaches (for the case of solution stability) are given. Illustrating examples are provided. (C) 2011 Elsevier Ltd. All rights reserved.
The aim of this paper is applying the scalarization technique to study some properties of the vector optimization problems under variable domination structure. We first introduce a nonlinear scalarization function of ...
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The aim of this paper is applying the scalarization technique to study some properties of the vector optimization problems under variable domination structure. We first introduce a nonlinear scalarization function of the vector-valued map and then study the relationships between the vector optimization problems under variable domination structure and its scalarized optimization problems. Moreover, we give the notions of DH-well-posedness and B-well-posedness under variable domination structure and prove that there exists a class of scalar problems whose well-posedness properties are equivalent to that of the original vector optimization problem.
In this paper, the semicontinuities of the solution set map are investigated for a parametric generalized vector quasivariational inequality in locally convex Hausdorff topological vector spaces. The upper semicontinu...
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In this paper, the semicontinuities of the solution set map are investigated for a parametric generalized vector quasivariational inequality in locally convex Hausdorff topological vector spaces. The upper semicontinuity and closedness of the solution set map are obtained. A parametric gap function is proposed by using a nonlinear scalarization function. By virtue of the parametric gap function and a key assumption, the Hausdorff lower semicontinuity of the solution set map is established. (C) 2010 Elsevier Ltd. All rights reserved.
In this paper, some gap functions for three classes of a system of generalized vector quasi-equilibrium problems with set-valued mappings (for short, SGVQEP) are investigated by virtue of the nonlinearscalarization f...
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In this paper, some gap functions for three classes of a system of generalized vector quasi-equilibrium problems with set-valued mappings (for short, SGVQEP) are investigated by virtue of the nonlinear scalarization function of Chen, Yang and Yu. Three examples are then provided to demonstrate these gap functions. Also, some gap functions for three classes of generalized finite dimensional vector equilibrium problems (GFVEP) are derived without using the nonlinear scalarization function method. Furthermore, a set-valued function is obtained as a gap function for one of (GFVEP) under certain assumptions.
In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in ...
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In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in this paper is a generalization of the corresponding result in [3].
This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Th...
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This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Then, from an existence theorem for a generalized quasi-equilibrium problem and a minimax inequality, existence theorems for two classes of generalized vector quasi-equilibrium problems are established.
This paper deals with generalized vector quasi-equilibrium problems. Using a so-called nonlinear scalarization function and a fixed point theorem, existence theorems for two classes of generalized vector quasi-equilib...
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This paper deals with generalized vector quasi-equilibrium problems. Using a so-called nonlinear scalarization function and a fixed point theorem, existence theorems for two classes of generalized vector quasi-equilibrium problems are established.
In this paper, we study generalized minimax inequalities in a Hausdorff topological vector space, in which the minimization and the maximization of a two-variable set-valued mapping are alternatively taken in the sens...
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In this paper, we study generalized minimax inequalities in a Hausdorff topological vector space, in which the minimization and the maximization of a two-variable set-valued mapping are alternatively taken in the sense of vector optimization. We establish two types of minimax inequalities by employing a nonlinear scalarization function and its strict monotonicity property. Our results are obtained under weaker convexity assumptions than those existing in the literature. Several examples are given to illustrate our results. (C) 2003 Elsevier Science (USA). All rights reserved.
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