本文選題：公共不動(dòng)點(diǎn) + 變分不等式　； 參考：《延安大學(xué)》2017年碩士論文

【摘要】：非線性算子的不動(dòng)點(diǎn)理論是非線性泛函分析研究的重點(diǎn)內(nèi)容之一.本文的重點(diǎn)內(nèi)容是構(gòu)造了新的迭代算法,分別用于逼近變分不等式的解,一族擬?-非擴(kuò)張映像的公共不動(dòng)點(diǎn)集與一族極大單調(diào)算子的公共零點(diǎn)集以及一個(gè)平衡問題解集的公共元素,并利用所構(gòu)造的新迭代算法證明了這幾種算法的強(qiáng)收斂性.所得結(jié)果改進(jìn)了國內(nèi)外在該方向中的一些相關(guān)成果.本文的主要內(nèi)容如下:第一部分:在一致光滑一致凸的Banach空間中,構(gòu)造了一種新的復(fù)合迭代算法,來逼近變分不等式的解,并借助Banach空間中的K-K性質(zhì)和廣義投影算法等方法證明了變分不等式解的強(qiáng)收斂定理.第二部分:在一致光滑嚴(yán)格凸具有K-K性質(zhì)的Banach空間中,構(gòu)造了一種新的收縮投影的迭代算法,來逼近一族擬?-非擴(kuò)張映像的公共不動(dòng)點(diǎn)集與一族極大單調(diào)算子的公共零點(diǎn)集以及一個(gè)平衡問題解集的公共元素,并利用所構(gòu)造的迭代算法證明了公共元素的強(qiáng)收斂性定理.作為應(yīng)用,給出了一個(gè)尋找變分不等式解的問題。
[Abstract]:The fixed point theory of nonlinear operators is one of the important contents of nonlinear functional analysis. In this paper, a new iterative algorithm is constructed, which is used to approximate the solutions of variational inequalities, respectively. The common fixed point set of a family of quasi -nonexpansive mappings, the common zero set of a family of maximal monotone operators and the common elements of a set of solutions to a equilibrium problem are discussed. The strong convergence of these algorithms is proved by using the new iterative algorithms constructed. The results obtained improve some related results in this direction at home and abroad. The main contents of this paper are as follows: the first part: in the uniformly smooth uniformly convex Banach space, a new compound iterative algorithm is constructed to approximate the solution of variational inequalities. The strong convergence theorem of solutions of variational inequalities is proved by means of K-K property and generalized projection algorithm in Banach spaces. In the second part, we construct a new iterative algorithm of contraction projection in Banach spaces with uniformly smooth strictly convex K-K property. The common fixed point set of a family of quasi-nonexpansive mappings, the common zero set of a family of maximal monotone operators and the common elements of the solution set of a equilibrium problem are approximated. The strong convergence theorem of common elements is proved by using the iterative algorithm constructed. As an application, a problem of finding solutions to variational inequalities is given.
【學(xué)位授予單位】：延安大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O177.91

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本文編號(hào)：2109970