弱拓扑下的非线性随机积分和微分方程组的解*

在本文中,我们首先对具有随机定义域的弱连续随机算子组证明了一个Darbo型随机不动点定理.利用这一定理,我们对Banach空间中关于弱拓扑的非线性随机Volterra积分方程组给出了随机解的存在性准则.作为应用,我们得到了非线性随机微分方程组的Canchy问题弱随机解的存在定理.也得到了这些随机方程组在Banach空间中关于弱拓扑的极值随机解的存在性和随机比较结果.我们的定理改进和推广了Szep,Mitchell－Smith,Cramer－Lakshmikantham,Lakshmikantham-Leela和丁的相应结果.     

Covering properties on H-spaces and applications

Several theorems on closed(resp.open)covering properties of H-spaces areobtained which improve and generalize the corresponding results of Sperner,Klee,Alexandroff-Pasynkoff,Berge,Ghouila-Houri,Danzer-Gr(?)nbaum-Klee,Ky Fan,Shih-Tan,Horvath and Lassonde.As application an almost fixed point theorem for lowersemi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed pointtheorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.     

Iterative construction of fixed points for multivalued operators of the monotone type in uniformly smooth Banach spaces

ＩＴＥＲＡＴＩＶＥＣＯＮＳＴＲＵＣＴＩＯＮＯＦＦＩＸＥＤＰＯＩＮＴＳＦＯＲＭＵＬＴＩＶＡＬＵＥＤＯＰＥＲＡＴＯＲＳＯＦＴＨＥＭＯＮＯＴＯＮＥＴＹＰＥＩＮＵＮＩＦＯＲＭＬＹＳＭＯＯＴＨＢＡＮＡＣＨＳＰＡＣＥＳＤｅｎｇＬｅｉ（邓磊）（ＣｈｏｎｇｑｉｎｇＴ...     

非线性随机积分和微分方程组的解*

在本文中我们首先对具有随机定义域的连续随机算子组证明了Darbao型不动点定理。应用此定理我们给出了非线性随机Volterra积分方程组和非线性随机微分方程组的Cauchy问题解的存在性准则。这些随机方程组的极值随机解的存在性和随机比较结果也被获得。我们的定理改进和推广Tyaughn,Lakshmikantham,Lakshmikantham-Leela,DeBlast-Myjak和第一作者的相应结果。     

自反Banach空间内混合非线性似变分不等式解的算法*

本文在自反Banach空间内研究了一类混合非线性似变分不等式应用作者得到的一个极小极大不等式,对这类混合非线性似变分不等式的解,证明了几个存在唯一性定理其次由应用辅助问题技巧,作者建议了一个计算此类混合非线性似变分不等式的近似解的创新算法最后讨论收敛性准则.     

Minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces

In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikanthamt and the results obtained by Lan in, and.     

Fixed points of nonexpansive mappings on star-shaped subsets of a convex metric space

In this paper, we give some characteristic properties of star-shaped sets which include a subset of a convex metric space. Using the characteristic properties, we discuss the existence problems of fixed points of nonexpansive type mappings on star-shaped subsets of convex metric spaces, which generalize the recent results obtained by Ding Xie-ping, Beg and Azam. Finally, we give an example which shows that our generalizations are essential.     

Random directional contractors and their applications

In this paper, as the generalizations of Altman’s directional contractors[4,5] and Lee and Padgett’s random contractors[1,2] we introduce the concept of random directional contractors for set-valued random operators. Using the new concept and transfinite induction, we show several existence theorems to solutions of nonlinear set-valued random operator equations. Our theorems improve and generalize the corresponding results in [1,2,4,5,11]. Next, some applications of our results to nonlinear random integral and differential equations are given.     

随机积分方程和微分方程解的存在性和比较结果

本文是[1]的继续.在本文中我们对非线性随机Volterra积分方程给出了解的另一存在性准则,极值解的存在性定理和随机积分不等式的比较定理,这些定理分别推广了Vaughan[2,3]和Lakshmikantham[4,5]的相应结果.     

多值映射的公共随机不动点定理

在本文中,我们对一般集值压缩型映射证明了几个随机公共不动点定理,这些定理改进和推广了[1～18]中的相应结果。