本文關(guān)鍵詞：局部凸空間凸性及不動(dòng)點(diǎn)定理的研究　出處：《天津理工大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 偶對(duì) P-自反 中點(diǎn)局部k-一致凸 有序規(guī)空間 距離函數(shù) -G度量空間

【摘要】：本文主要研究的是局部凸空間的凸性和光滑性及兩類空間中的不動(dòng)點(diǎn)問題及其應(yīng)用.一是局部凸空間,在局部凸空間已有的中點(diǎn)局部k-一致光滑性和中點(diǎn)局部k-一致凸性這一對(duì)概念的基礎(chǔ)上,證明了中點(diǎn)局部k-一致凸性和中點(diǎn)局部(k+1)-一致凸性之間的關(guān)系,并給出了在P-自反的條件下他們之間的等價(jià)對(duì)偶定理.二是有序規(guī)空間,在循環(huán)(ψλ,A,B)-映射條件下的不動(dòng)點(diǎn)定理.三是G-度量空間,在距離函數(shù)有關(guān)條件下的不動(dòng)點(diǎn)定理及其應(yīng)用.第一章,介紹了局部凸空間的概念及性質(zhì),本章將多種凸性(光滑性)之間的關(guān)系加以梳理,證明了中點(diǎn)局部k-一致凸性蘊(yùn)含中點(diǎn)局部(k+1)-一致凸性即：(1)若(X,P)是中點(diǎn)局部k-一致凸的,則(X,P)是中點(diǎn)局部k+1-一致凸的；(2)若(X,P)是中點(diǎn)局部k-一致光滑的,則(X,P)是中點(diǎn)局部k+1-一致光滑的.最后證明了在(X,TP))在P-自反的條件下的對(duì)偶性：(1)(X',P*)是中點(diǎn)局部k-一致凸的,當(dāng)且僅當(dāng)(X,P)是中點(diǎn)局部k-一致光滑的；(2)(X',P*)是中點(diǎn)局部k-一致光滑的,當(dāng)且僅當(dāng)(X,P)是中點(diǎn)局部k-一致凸的.第二章,介紹了有序規(guī)空間的概念及性質(zhì),討論了(ψλ,A,B)循環(huán)壓縮映射條件下公共不動(dòng)點(diǎn)定理.有序規(guī)空間(X,τ,(?)),A,B是X的閉子集,映射f,g:X→X為(A,B)-弱增的,假設(shè)(1)(f,g)為(ψλ,A,B)-循環(huán)壓縮映射；(2)f或g是連續(xù)的.則f,g有公共不動(dòng)點(diǎn).第三章,介紹了G-度量空間中的概念與性質(zhì)及不動(dòng)點(diǎn)定理方面的一個(gè)推論.G-度量空間(X,G),對(duì)所有x,y,z ∈X,X上映射f滿足不等式其中0δ,α1,則f有不動(dòng)點(diǎn)u ∈X然后利用所得結(jié)論解決一個(gè)非線性積分方程有唯一解的問題.積分方程：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，

本文編號(hào)：1364625