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In this paper, we give a characterization of an order ideal which is not necessarily positively generated in the ordered space of Hermitian matrices. Order properties for perfect subspaces are also studied along with other subspace order properties.
A robust optimization problem, which has a maxi-mum function of continuously differentiable functions as its objective function, continuously differentiable functions as its constraint functions and a geometric constraint, is considered. We prove a necessary optimality theorem and a sufficient optimality theorem for the robust optimization problem. We formulate a Wolfe type dual problem for the robust optimization problem, which has a differen-tiable Lagrangean function, and establish the weak duality theorem and the strong duality theorem which hold between the robust optimization problem and its Wolfe type dual problem. Moreover, saddle point theorems for the robust optimization problem are given under convexity assumptions.
A generalized quadratic fuzzy set is a generalization of a quadratic fuzzy number. Zadeh dees the probability of the fuzzy event using the probability. We dee the normal fuzzy prob-ability on R using the normal distribution. And we calculate the normal fuzzy probability for generalized quadratic fuzzy sets.
In this paper, we investigate some properties of 2-norm midpoints and 2-normed equalities in 2-normed spaces.
Fuzzy measures in this paper are a class of distortedLebesgue measures (see ). We investigate some properties of thederivatives with respect to distorted Lebesgue measures and givesome important examples.
Park, Ryu, and Lee recently defined a Henstock-type integral, which lies entirely between the McShane and the Henstock integrals. This paper presents two characterizing convergence conditions for this integral, and derives other known convergence theorems as corollaries.
In this paper, we prove the generalized Hyers-Ulam stability for the following additive-quadratic functional equation f(2x + y) + f(2x y) = f(x + y) + f(x y) + 4f(x) + 2f( x) in modular spaces by using a xed point theorem for modular spaces.