A drop theorem without vector topology

Daneš' drop theorem is extended to bornological vector spaces. An immediate application is to establish Ekeland-type variational principle and its equivalence, Caristi fixed point theorem, in bornological vector spaces. Meanwhile, since every locally convex space becomes a convex bornological vector space when equipped with the canonical von Neumann bornology, Qiu's generalization of Daneš' work to locally convex spaces is recovered.     

Vectorial form of Ekeland-type variational principle with applications to vector equilibrium problems and fixed point theory

This paper introduces a vectorial form of equilibrium version of Ekeland-type variational principle. Some equivalent results to our variational principle are given. As applications, we derive the existence of solutions of a vector equilibrium problem in the setting of complete quasi-metric spaces with a W-distance. Caristi-Kirk fixed point theorem for multivalued maps is also established in a more general setting.     

Existence results for systems of strong implicit vector variational inequalities

The purpose of this paper is to introduce and study systems of strong implicit vector variational inequalities. Under suitable conditions, some existence results for systems of strong implicit vector variational inequalities are established by the Kakutani--Fan--Glicksberg fixed point theorem. This revised version was published online in June 2006 with corrections to the Cover Date.     

度量空间和锥度量空间中的若干不动点定理

给出了度量空间和锥度量空间中的若干不动点定理.利用这些不动点定理,统一并推广了度量空间和锥度量空间中的若干经典的不动点定理.     

Super efficiency in convex vector optimization

We establish a Lagrange Multiplier Theorem for super efficiency in convex vector optimization and express super efficient solutions as saddle points of appropriate Lagrangian functions. An example is given to show that the boundedness of the base of the ordering cone is essential for the existence of super efficient points.Research is supported partially by NSERC.Research is supported partially by NSERC and Mount St. Vincent University grant.     

On the notion of proper efficiency in vector optimization

In this paper, we consider the main definitions of proper efficiency for a vector optimization problem in topological linear spaces. The implications among these definitions generalize the inclusion structure holding in Euclidean spaces with componentwise ordering.     

实线性锥距离空间中带有锥W-距离的不动点定理

在实线性锥距离空间中给出锥、W-距离的概念及一些性质．由此在实线性锥距离空间中建立了压缩型和扩张型两类不动点定理,其中压缩条件和扩张条件中均含有锥W-距离．     

Complete efficiency and interdependencies between objective functions in vector optimization

Summary Vector optimization problems in linear spaces with respect to general domination sets are investigated including corollaries to Pareto-optimality and weak efficiency. The results contain equivalences between vector optimization problems, interdependencies between objective functions and domination sets, statements about the influence of perturbed objective functions on the decision maker's preferences and thus on the domination set, comparisons of efficiency with respect to polyhedral cones with Pareto-optimality, changes in the objective functions which restrict, extend or do not alter the set of Pareto-optima, possibilities for the use of domination sets immediately in the decision space. Conditions for complete efficiency are given.

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Zusammenfassung Untersucht werden Vektoroptimierungsprobleme in linearen Räumen bezüglich allgemeiner Dominanzmengen einschließlich Folgerungen für Pareto-Optimalität und schwache Effizienz. Die Ergebnisse enthalten Äquivalenzen zwischen Vektoroptimierungsproblemen, Wechselwirkungen zwischen Zielfunktionen und Dominanzmengen, Aussagen über den Einfluß gestörter Zielfunktionen auf die Präferenzen des Entscheidungsträgers und somit auf die Dominanzmenge, Vergleiche von Effizienz bezüglich polyedrischer Kegel mit Pareto-Optimalität, Änderungen in den Zielfunktionen, die die Menge der Pareto-Optima einschränken, erweitern oder nicht beeinflussen, Möglichkeiten für die Nutzung von Dominanzmengen unmittelbar im Entscheidungsraum. Bedingungen für vollständige Effizienz werden gegeben.

     

对称向量拟均衡问题有效解的存在性

利用标量化方法建立对称向量拟均衡问题有效解的存在性定理.作为标量化方法的应用,利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理.     

一类积集上的广义向量变分不等式

研究一类积集上具某种权向量的广义向量变分不等式组及其广义向量变分不等式的有关问题,刻画它们之间解的相互关系.在映射的次连续性和关于某向量广义单调性的条件下,利用集值映射的不动点定理,对所讨论的几种类型的广义向量变分不等式给出解的存在性.     

An existence theorem of positive solutions for elastic beam equation with both fixed end-points

Abstract. By using the degree theory on cone an existence theorem of positive solution for aclass of fourth-order two-point BVP‘s is obtained. This class of BVP‘s usually describes the de-formation of the elastic beam with both fixed end-points.     

非线性分数微分方程解的若干存在性结论

研究了非线性分数微分方程解的存在性,通过考察非线性项在无穷远处的增长或者非线性项在某个有界集上的“高度”获得了若干新的存在性结论,主要工具是Schauder不动点定理和Leray-Schauder不动点定理．     

Caristi 不动点定理的推广及应用

本文推广了古典的Garisti不动点定理,作为应用,古典的Ekeland变分原理得到了推广,并且证明了推广的Garisti不动点定理和推广的Ekeland变分原理是等价的．     

A result on sets,with applications to vector optimization

In this paper there is stated a result on sets in ordered linear spaces which can be used to show that some properties of the sets are inherited by their convex hulls under suitable conditions. As applications one gives a characterization of weakly efficient points and a duality result for nonconvex vector optimization problems.