局部凸空间凸性及不动点定理的研究

发布时间：2018-01-01 13:08

  本文关键词：局部凸空间凸性及不动点定理的研究　出处：《天津理工大学》2015年硕士论文　论文类型：学位论文

  更多相关文章： 偶对 P-自反 中点局部k-一致凸 有序规空间 距离函数 -G度量空间

【摘要】：本文主要研究的是局部凸空间的凸性和光滑性及两类空间中的不动点问题及其应用.一是局部凸空间,在局部凸空间已有的中点局部k-一致光滑性和中点局部k-一致凸性这一对概念的基础上,证明了中点局部k-一致凸性和中点局部(k+1)-一致凸性之间的关系,并给出了在P-自反的条件下他们之间的等价对偶定理.二是有序规空间,在循环(ψλ,A,B)-映射条件下的不动点定理.三是G-度量空间,在距离函数有关条件下的不动点定理及其应用.第一章,介绍了局部凸空间的概念及性质,本章将多种凸性(光滑性)之间的关系加以梳理,证明了中点局部k-一致凸性蕴含中点局部(k+1)-一致凸性即：(1)若(X,P)是中点局部k-一致凸的,则(X,P)是中点局部k+1-一致凸的；(2)若(X,P)是中点局部k-一致光滑的,则(X,P)是中点局部k+1-一致光滑的.最后证明了在(X,TP))在P-自反的条件下的对偶性：(1)(X',P*)是中点局部k-一致凸的,当且仅当(X,P)是中点局部k-一致光滑的；(2)(X',P*)是中点局部k-一致光滑的,当且仅当(X,P)是中点局部k-一致凸的.第二章,介绍了有序规空间的概念及性质,讨论了(ψλ,A,B)循环压缩映射条件下公共不动点定理.有序规空间(X,τ,(?)),A,B是X的闭子集,映射f,g:X→X为(A,B)-弱增的,假设(1)(f,g)为(ψλ,A,B)-循环压缩映射；(2)f或g是连续的.则f,g有公共不动点.第三章,介绍了G-度量空间中的概念与性质及不动点定理方面的一个推论.G-度量空间(X,G),对所有x,y,z ∈X,X上映射f满足不等式其中0δ,α1,则f有不动点u ∈X然后利用所得结论解决一个非线性积分方程有唯一解的问题.积分方程：其中K:[0,T]×[0,T]×R→R,h:R→R.
[Abstract]:This paper mainly studies the locally convex space convexity and smoothness and two kinds of space in the fixed point problem and its application. One is a locally convex space, which is based on the concept of midpoint locally k- locally convex space has uniform smoothness and midpoint locally k- uniformly convexity and midpoint locally k- proved uniform convexity and midpoint locally (k+1) - the relationship between the uniform convexity, and gives the equivalent duality theorem under the condition of P- reflexivity between them. The two is ordered metric space and in circulation (PSI lambda, A, B) - mapping under the condition of fixed point theorem. Three is the G- metric space. In the distance function under the condition of fixed point theorem and its application. The first chapter introduces the concept and properties of locally convex spaces, this chapter will be a variety of convexity (smoothness) relationship between combs, proved that the midpoint locally k- uniformly convex (k+1) contains the midpoint locally uniform convexity (namely: - 1) 鑻，

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