Gue Myung Lee

Generalized vector variational inequality and fuzzy extension

Abstract A generalized vector variational inequality (GVVI) is considered. We establish the existence theorem for (GVVI) under assumptions of C -pseudomonotonicity and V -hemicontinuity. From our existence theorem, we obtain the fuzzy extension of a result of Chen and Yang.

Generalized vector variational inequality

A generalized vector variational inequality (GVVI) is considered. We establish the existence theorem for solutions of (GVVI) with H-convexity assumption. Our existence theorem extends that of Chen [1, Theorem 3.1] to the set-valued case.

Duality for multiobjective programming involving n-set functions

We formulate the Wolfe, Mond-Weir and generalized Mond-Weir types of dual problems for a multiobjective program involving vector valued n-set functions. By using the concept of efficiency (Pareto optimum) we prove the weak and strong duality theorems for a multiobjective program under generalized ρ-convexity assumptions.

Fixed degree and fixed point theorems for fuzzy mappings in probabilistic metric spaces

Abstract This paper introduces the concept and properties of fixed degrees for fuzzy mappings in probabilistic metric spaces. By virtue of this concept, some theorems about common fixed degree of a sequence of fuzzy mappings in probabilistic metric spaces are obtained. These new results are a unified approach to generalize several fixed point theorems for fuzzy mappings.

Duality for multiobjective fractional programming involving n-set functions sup *

For a multiobjective fractional programming problem (MFP) involving vector valued n-set functions, the dual problem (MFD) and the generalized dual problem (GMFD) are formulated and the concept of efficiency is used to prove the weak, strong and strict converse duality results between the associated parametric problem (MFP) λ and (MFD) under generalized ρ-convexity assumptions. Also, those duality results between (MFP) λ, and (GMFD) are obtained

Generalized trade-off directions in multiobjective optimization problems

Abstract In this brief paper, we define the generalized trade-off directions for a multiobjective optimization problem (MP), by using the contingent cone, and characterize the set of generalized trade-off directions for the problem (MP), by using the sensitivity results of Tanino [1].

Vector quasivariational inequalities for fuzzy mappings (II)

Abstract This paper is devoted to study the vector variational inequalities for fuzzy mappings. By using the Fan-Browder fixed point theorem, the selection theorem of Yannelis-Prabhakar [13] and the scalarization method of Luc [9,10], some existence theorems for our inequalities are proved.

SADDLE POINTS AND MINIMAX THEOREMS FOR VECTOR-VALUED MULTIFUNCTIONS ON H-SPACES

Abstract In this paper some existence theorems of loose saddle point, saddle point, and minimax problems for vector-valued multifunctions on H -spaces are proved. The results presented in this paper generalize some recent results in [1–4].

Strongly quasivariational inequalities for fuzzy mappings

Abstract We consider a strongly quasivariational inequality problem for fuzzy mappings. A projection technique is used to suggest an iterative algorithm for finding the approximate solutions for our problem and prove that the approximate solution converges strongly to the exact solution for our problem.

Optimality for nonlinear programs containing n-set functions

Abstract Under the generalized (ℑ, ρ, θ)-convexity assumptions, we establish the sufficient optimality conditions for the nonlinear programs with vector-valued n-set functions on the inequality and equality constraints.