共查询到20条相似文献,搜索用时 406 毫秒
1.
§ 1. Introduction Theconvexfunctionshavebeenextensivelystudiedinonecomplexvariable .Thesefunc tionsareeasilycharacterizedbysimpleanalyticorgeometricconditionsandtherearemanywellknownresultswhichcanhelpusunderstandtheirnature.However,thedifficultiesariseinsev eralcomplexvariables.Imposingtheconditionthatamappingbeconvexmappingturnsouttobeveryrestrictiveandsothefamilyofquasi convexmappingswasintroducedbyROPERKAandSUFFRIDGETJin [1 ].In [2 ]wehaveshown :thefamilyofquasi convexmappings… 相似文献
2.
一类非线性椭圆边值问题解的存在性 总被引:12,自引:5,他引:7
魏利 《数学的实践与认识》2001,31(3):360-364
目前 ,对 s——拉普拉斯算子△s的研究是较为活跃的数学课题 .原因在于算子 -△s与许多物理现象有关 .比如 :反射扩散问题 ,石油提取问题等等 .基于此因 ,在文 [3]的基础上 ,我们将继续研究以下非线性边值问题在 Ls(Ω) ,( 1 2 nn+1 )中解的存在条件 .-△su +g( x,u) =f几乎处处在Ω中-〈 ,| u|s- 2 u〉 =0几乎处处在Γ上其中 f∈Ls( Ω)给定 ,Ω Rn( n 1 ) ,△su=div( | u|s- 2 u) ,g∶Ω× R→ R满足 Caratheodory条件 .本文把文 [3]关于非线性边值问题 @在 Lp( Ω) ( 2 p<+∞ )空间中解的存在性的研究推广到 Ls( Ω) ( 1 2 nn+1 )空间中 . 相似文献
3.
4.
关于线性空间到欧氏空间的映射与线性映射 总被引:1,自引:0,他引:1
文[2]推广了文[1]的全部定理,文[3]又推广了文[2]的全部定理,本文进一步推广了文[3]的全部定理,且证法简洁明快.本文约定,若V,ω是线性空间,则Vω表示V到ω的所有映射的集合,L(Vω)表示所有V到ω的线性映射的集合,L(V)表示V的所有线性变换的集合.本文总假定V是实数域上的线性空间,ω,ω1,ω2,…,ωn为欧氏空间.引理1 设A,B∈Vω,Ct,Dt∈Vωt(t=1,2,…,n),若α,β∈V有(Aα,Bβ)=∑nt=1(Ctα,Dtβ)(1)则x1,x2,…,xr, y1,y2,...,ys∈R(r,s∈N)α1,α2,…,αr, β1,β2,...,βs∈V,有(∑ri=1xiAαi,∑sj=1yjBβj)=∑nt=1(∑ri=1x… 相似文献
5.
6.
Wehaveintroducedσconstructionofrings[1],[2]withhomomorphismofmodulesofringsinringtheoryanddiscussedsomerelationsbetweenringRand[R]σandRσ.Thecongruencesandidealsareequevalent,sohomomorphismsandidealsarecorrespondingonebyoneinringtheory;buthomomorphismsandidealsarenotequevalentinsemigrouptheory,homomor-phismsandcongreuncesarecorrespondingonebyone,thekernerofhomomorphismsisacon-greunces,hencethediscussionofsimilarproblemsinringtheoryandsemigrouptheoryhasgreatdifference.Firstweintroducethenoti… 相似文献
7.
A.du Plessis[1]对实奇点理论中?决定的阶数作了很好的估计。T.Ga-ffney等[2]发展到I-?及M-?的情形。李养成[4]则将[1]向?_k作了推广。本文以[2]为特例,也推广了[4]的部分结果。作为推论,本文建立了∞-?_k的一个估计,当k=0是[7]的主要结果。§4例说明[1]的定理(2.8)不能推广到M情况。 相似文献
8.
9.
文献[8]提出了一类基于分层量化的偏序集结构(以下简称R-偏序集).此结构是sfe[5]的非对称推广,也是拟度量空间(quasi-metric spaces,qms)[3]和广义超度量空间(generalized ultrametric spaces,gums)[4]的一种特殊情形.本文定义了其上的广义Alexande... 相似文献
10.
§ 1. Introduction SinceDAUBECHIES [1 ]gavethewellknownconstructionofunivariatecompactlysup portedorthonormalwavelets,considerableattertionhasbeenspentonconstructingmultivariatecompactlysupportedorthonormalwavelets [2— 5etc.] .Althoughmanyspecialbivariatenon separablewaveletshavebeenconstructed ,itisstillanopenproblemhowtoconstructbivariatecompactlyorthonormalwaveletsforanygivencompactlysupportedscalingfunction .Thepur poseofthispaperistoconstructcompactlysupportedorthogonalwaveletass… 相似文献
11.
This paper deals with the stability properties of those set-valued mappings from locally metrizable spaces to Euclidean spaces for which the images are the convex hull of their boundaries (i.e., they are closed convex sets not containing a halfspace). Examples of this class of mappings are the feasible set and the optimal set of convex optimization problems, and the solution set of convex systems, when the data are subject to perturbations. More in detail, we associate with the given set-valued mapping its corresponding boundary mapping and we analyze the transmission of the stability properties (lower and upper semicontinuity, continuity and closedness) from the given mapping to its boundary and vice versa. 相似文献
12.
We extend our work on the optimal mapping of distributions in three directions: (a) we consider any set-valued mapping, not just diffeomorphisms; (b) we distinguish between weak and strong optimality, and identify strong optimality with cyclic monotonicity; and (c) we prove that, under some restrictions, a weakly optimal mapping has the subgradient property. 相似文献
13.
T. S. Angell 《Journal of Optimization Theory and Applications》1985,46(2):129-151
We prove the existence of a solution of an integral inclusion of Urysohn type with delay. By imposing standard boundedness, convexity, and semicontinuity conditions on the set-valued mapping defining the integral inclusion, we show that the right-hand side of the relation constitutes a mapping defined on a suitable Banach space and satisfying the conditions of Kakutani's theorem for the existence of a fixed point of a set-valued mapping. By introducing the notion of generalized or chattering state solutions, we show how the convexity requirements may be relaxed.This work was supported by NSF Grant No. MCS-82-02033. 相似文献
14.
集值映射多目标规划问题的解集的连通性 总被引:6,自引:2,他引:4
傅万涛 《高校应用数学学报(A辑)》1994,(3):321-328
本文研究了无限维空间里集值映射的多目标规划问题。主要结果是:当目标函数为类凸的集值映射时,其目标空间里的有效点集是连通的;若目标函数为C-凸的集值映射时,其有效解集也连通。 相似文献
15.
Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities 总被引:3,自引:0,他引:3
The variational inequality problem with set-valued mappings is very useful in economics and nonsmooth optimization. In this paper, we study the existence of solutions and the formulation of solution methods for vector variational inequalities (VVI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence of a solution of the VVI. It is shown that the optimization problem formulated by using gap functions can be transformed into a semi-infinite programming problem. We investigate also the existence of a solution for the generalized VVI with a set-valued mapping by virtue of the existence of a solution of the VVI with a single-valued function and a continuous selection theorem. 相似文献
16.
S. K. Mishra S. Y. Wang K. K. Lai 《Journal of Optimization Theory and Applications》2008,138(1):77-84
Variational-like inequalities with set-valued mappings are very useful in economics and nonsmooth optimization problems. In
this paper, we study the existence of solutions and the formulation of solution methods for vector variational-like inequalities
(VVLI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence
of a solution of the VVLI. We investigate the existence of a solution for the generalized VVLI with a set-valued mapping by
exploiting the existence of a solution of the VVLI with a single-valued function and a continuous selection theorem.
The research of first author was partially supported by the Council of Scientific and Industrial Research, New Delhi, Ministry
of Human Resources Development, Government of India Grant 25(0132)/ER-II/2004. 相似文献
17.
《Optimization》2012,61(4):389-399
We study the stability of a Hummel–Seebeck like method for solving variational inclusions of the form 0?∈?f(x)?+?G(x), where f is a single-valued function while G stands for a set-valued mapping, both of them acting in Banach spaces. Then, we investigate a measure of conditioning of these inclusions under canonical perturbations. 相似文献
18.
《Optimization》2012,61(6):763-780
The notion of covering is introduced for a set-valued mapping defined on an arbitrary set in a Banach space. A necessary and sufficient covering criterion is proved. The conditions are formulated in terms of generalized differentials and generalized normals. The covering theorem is applied to deduce formulas of generalized differential calculus and necessary optimality conditions for nonsroooth optimization problems. 相似文献
19.
X. P. Ding 《Journal of Optimization Theory and Applications》1997,95(3):601-613
In this paper, we introduce a new class of generalized variational-like inequalities involving a nonmonotone-type set-valued mapping which is more general than those in the known literature. By applying a KKM-type theorem established by the author, some existence theorems for the solutions to the class of generalized variational-like inequalities are proved in Hausdorff locally convex topological vector spaces. 相似文献
20.
A. Y. Azimov 《Journal of Optimization Theory and Applications》2008,137(1):61-74
The duality of multiobjective problems is studied with the help of the apparatus of conjugate set-valued mappings introduced
by the author. In this paper (Part 1), a duality theory is developed for set-valued mappings, which is then used to derive
dual relations for some general multiobjective optimization problems which include convex programming and optimal control
problems. Using this result, in the companion paper (Part 2), duality theorems are proved for multiobjective quasilinear and
linear optimal control problems. The theory is applied to get dual relations for some multiobjective optimal control problem. 相似文献