一类三角级数的最佳逼近度“双边”单调性条件的重要应用

在本质性推广了O-正则变化拟单调性的一个新条件下,本文在一般复值连续函数空间给出了一类三角级数最佳逼近度的完整结果,并建立了一个重要应用．     

A remark on ``two-sided' monotonicity condition: an application to L p convergence

Summary To verify the universal validity of the ``two-sided' monotonicity condition introduced in [4], we will apply it to include more classical examples. The present paper selects the L^p convergence case for this purpose. Furthermore, Theorem 3 shows that our improvements are not trivial.     

A Result on Localization of Equilibria

In this paper, we deal with a general equilibrium problem where a bimap F: A×B X×Y2 ^Z is involved. This problem contains the scalar equilibrium problem as a very special case. The general equilibrium is considered via the properties of the map G: B2 ^A naturally associated to the problem. The main result shows that, to have solutions on every convex subsets B ₁ of B, localized via a map T: B2 ^A , a necessary and sufficient condition is the KKM property of the map G with respect to T. The assumptions require that T satisfies a regularity condition with respect to G, and it is proved that this condition is quite sharp, providing a suitable counterexample.     

A Note on Equilibrium Problems with Properly Quasimonotone Bifunctions

In this paper, we consider some well-known equilibrium problems and their duals in a topological Hausdorff vector space X for a bifunction F defined on K x K,where K is a convex subset of X. Some necessary conditions are investigated, proving different results depending on the behaviour of F on the diagonal set. The concept of proper quasimonotonicity for bifunctions is defined, and the relationship with generalized monotonicity is investigated. The main result proves that the condition of proper quasimonotonicity is sharp in order to solve the dual equilibrium problem on every convex set.     

Vector Equilibrium Problems with Generalized Monotone Bifunctions

A 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 locally convex vector space, find x ^*K such that for all yK. This problem generalizes the (scalar) equilibrium problem and the vector variational inequality problem. Extending very recent results for these two special cases, the paper establishes existence of solutions for the unifying model, assuming that F is either a pseudomonotone or quasimonotone bifunction.     

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 the operatorf are weakened and, in some results, the regularity assumptions on the domain off are relaxed significantly. The concept of inner point for subsets of Banach spaces proves to be useful.This work was completed while the first author was visiting the Graduate School of Management of the University of California, Riverside. The author wishes to thank the School for its hospitality.     

Hartman-Mycielski functor of non-metrizable compacta

We investigate certain topological properties of the normal functor H, introduced by the first author, which is a certain functorial compactification of the Hartman-Mycielski construction HM. We prove that H is always open and we also find the condition when H X is an absolute retract, homeomorphic to the Tychonov cube.     

Vectorization hierarchies of some graph quantifiers

We give a sufficient condition for the inexpressibility of the k-th extended vectorization of a generalized quantifier in , the extension of first-order logic by all k-ary quantifiers. The condition is based on a model construction which, given two -equivalent models with certain additional structure, yields a pair of -equivalent models. We also consider some applications of this condition to quantifiers that correspond to graph properties, such as connectivity and planarity. Received: 15 October 1996     

On stably quasimonotone hemivariational inequalities

We establish some existence results for variational-hemivariational inequalities of the Hartman-Stampacchia type involving stably quasimonotone set-valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive a sufficient condition for the existence and boundedness of solutions.     

Multiplicative perturbations in semigroup theory with the (Z)-condition

In [4] the (Z)-condition was introduced by G. W. Desch and W. Schappacher. This condition on a Banach spaceZ and a generatorA inX ensures thatA(I+B) and(I+B)A generateC ₀-semigroups, ifB has its range inZ. In this paper we will consider how certain properties of the semigroup generated byA are inherited by the semigroups generated byA(I+B) and(I+B)A. We shall furthermore investigate a related condition, that simplifies certain sufficiency assumptions given previously.