This paper establishes the stable results for generalized fuzzy games by using a nonlinearscalarization technique. The authors introduce some concepts of well-posedness for generalized fuzzy games. Moreover, the auth...
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This paper establishes the stable results for generalized fuzzy games by using a nonlinearscalarization technique. The authors introduce some concepts of well-posedness for generalized fuzzy games. Moreover, the authors identify a class of generalized fuzzy games such that every element of the collection is generalized well-posed, and there exists a dense residual subset of the collection, where every generalized fuzzy game is robust well-posed.
This work is devoted to examining inverse vector variational inequalities with constraints by means of a prominent nonlinear scalarizing functional. We show that inverse vector variational inequalities are equivalent ...
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This work is devoted to examining inverse vector variational inequalities with constraints by means of a prominent nonlinear scalarizing functional. We show that inverse vector variational inequalities are equivalent to multiobjective optimization problems with a variable domination structure. Moreover, we introduce a nonlinearfunction based on a well-known nonlinear scalarization function. We show that this function is a weak separation function and a regular weak separation function under different parameter sets. Then two alternative theorems are established, which will provide the basis for characterizing efficient elements of inverse vector variational inequalities.
In this paper, we consider three kinds of pointwise well-posedness for set optimization problems. We establish some relations among the three kinds of pointwise well-posedness. By virtue of a generalized nonlinear sca...
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In this paper, we consider three kinds of pointwise well-posedness for set optimization problems. We establish some relations among the three kinds of pointwise well-posedness. By virtue of a generalized nonlinear scalarization function, we obtain the equivalence relations between the three kinds of pointwise well-posedness for set optimization problems and the well-posedness of three kinds of scalar optimization problems, respectively.
In this paper, we consider well-posedness of symmetric vector quasi-equilibrium problems. Based on a nonlinearscalarization technique, we first establish the bounded rationality model M for symmetric vector quasi-equ...
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In this paper, we consider well-posedness of symmetric vector quasi-equilibrium problems. Based on a nonlinearscalarization technique, we first establish the bounded rationality model M for symmetric vector quasi-equilibrium problems, and then introduce a well-posedness concept for symmetric vector quasi-equilibrium problems, which unifies its Hadamard and Tykhonov well-posedness. Finally, sufficient conditions on the well-posedness for symmetric vector quasi-equilibrium problems are given.
This paper is devoted to the semicontinuity of solutions of a parametric generalized Minty vector quasivariational inequality problem with set-valued mappings [(in short (PGMVQVI)] in Hausdorff topological vector spac...
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This paper is devoted to the semicontinuity of solutions of a parametric generalized Minty vector quasivariational inequality problem with set-valued mappings [(in short (PGMVQVI)] in Hausdorff topological vector spaces, when the mapping and the constraint sets are perturbed by different parameters. The upper (lower) semicontinuity and closedness of the solution set mapping for (PGMVQVI) are established under some appropriate assumptions. The sufficient and necessary conditions of the Hausdorff lower semicontinuity and Hausdorff continuity of the solution set mapping for (PGMVQVI) are also derived without monotonicity. As an application, we discuss the upper semicontinuity for the solution set mapping of a special case of the (PGMVQVI).
Recently, Du (J nonlinear Anal 72:2259-2261, 2010) by using a nonlinear scalarization function, in the setting of locally convex topological vector spaces, could transfer a cone metric space to a usual metric space. S...
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Recently, Du (J nonlinear Anal 72:2259-2261, 2010) by using a nonlinear scalarization function, in the setting of locally convex topological vector spaces, could transfer a cone metric space to a usual metric space. Simultaneously, Amini-Harandi and Fakhar (Com Math Appl 59:3529-3534, 2010) by using a notion of base for the cone , in the setting of Banach spaces, could do the same. In this note we will see that two methods coincide and moreover they are valid for topological vector spaces and it is not necessary that we only consider the cones which have a compact base. Finally, it is worth noting that the nature of this note is similar to Caglar and Ercan (Order-unit-metric spaces, arXiv:1305.6070 [***], 2013).
In this paper, we establish the bounded rationality model M for generalized vector equilibrium problems by using a nonlinearscalarization technique. By using the model M, we introduce a new well-posedness concept for...
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In this paper, we establish the bounded rationality model M for generalized vector equilibrium problems by using a nonlinearscalarization technique. By using the model M, we introduce a new well-posedness concept for generalized vector equilibrium problems, which unifies its Hadamard and Levitin-Polyak well-posedness. Furthermore, sufficient conditions for the well-posedness for generalized vector equilibrium problems are given. As an application, sufficient conditions on the well-posedness for generalized equilibrium problems are obtained.
This paper gives sufficient conditions for the continuity of the solution mappings of parametric non-weak vector Ky Fan inequality problems with moving cones. The main results of the paper are new and are obtained und...
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This paper gives sufficient conditions for the continuity of the solution mappings of parametric non-weak vector Ky Fan inequality problems with moving cones. The main results of the paper are new and are obtained under an assumption different from the known density hypothesis. They are written in terms of nonlinear scalarization functions associated to the data of the problems under consideration. Verifiable conditions are given, and examples are provided.
This paper is devoted to the Levitin-Polyak well-posedness by perturbations for a class of general systems of set-valued vector quasi-equilibrium problems (SSVQEP) in Hausdorff topological vector spaces. Existence of ...
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This paper is devoted to the Levitin-Polyak well-posedness by perturbations for a class of general systems of set-valued vector quasi-equilibrium problems (SSVQEP) in Hausdorff topological vector spaces. Existence of solution for the system of set-valued vector quasi-equilibrium problem with respect to a parameter (PSSVQEP) and its dual problem are established. Some sufficient and necessary conditions for the Levitin-Polyak well-posedness by perturbations are derived by the method of continuous selection. We also explore the relationships among these Levitin-Polyak well-posedness by perturbations, the existence and uniqueness of solution to (SSVQEP). By virtue of the nonlinearscalarization technique, a parametric gap function g for (PSSVQEP) is introduced, which is distinct from that of Peng (J Glob Optim 52:779-795, 2012). The continuity of the parametric gap function g is proved. Finally, the relations between these Levitin-Polyak well-posedness by perturbations of (SSVQEP) and that of a corresponding minimization problem with functional constraints are also established under quite mild assumptions.
This paper gives sufficient conditions for the upper and lower semicontinuities of the solution mapping of a parametric mixed generalized Ky Fan inequality problem. We use a new scalarizing approach quite different fr...
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This paper gives sufficient conditions for the upper and lower semicontinuities of the solution mapping of a parametric mixed generalized Ky Fan inequality problem. We use a new scalarizing approach quite different from traditional linear scalarization approaches which, in the framework of the stability analysis of solution mappings of equilibrium problems, were useful only for weak vector equilibrium problems and only under some convexity and strict monotonicity assumptions. The main tools of our approach are provided by two generalized versions of the nonlinear scalarization function of Gerstewitz. Our stability results are new and are obtained by a unified technique. An example is given to show that our results can be applied, while some corresponding earlier results cannot.
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