發(fā)布時(shí)間：2018-04-17 07:10

  本文選題：n-Banach空間 + 壓縮映射��； 參考：《西北大學(xué)》2017年碩士論文

【摘要】：不動(dòng)點(diǎn)理論實(shí)際是算子方程Tx = x的求解問(wèn)題,是解決許多代數(shù)方程,積分方程,微分方程解的存在唯一性的理論基礎(chǔ),是泛函分析中的重要內(nèi)容之一.本文利用迭代法,構(gòu)造n-Banach空間上的收斂序列,證明了n-Banach空間中壓縮映射不動(dòng)點(diǎn)的存在性和唯一性,從而推廣和改進(jìn)了文獻(xiàn)中的一些結(jié)論,所取得的主要成果如下:1.在n-Banach空間中,將經(jīng)典壓縮的映射ρ(Tx,Ty)≤θρ(x,y),θ∈[0,1)中常數(shù)θ推廣為[0,+∞)到[0,1)內(nèi)的一元函數(shù)f(t),得出了:|| Tx-Ty,c1,…,Cn-1 ||≤ f(||x-y,c1,…,cn-1||)|| x-y,c1,…,cn-1 ||從而證明了的幾類不同壓縮映射的不動(dòng)點(diǎn)定理.2.在n-Banach空間中,根據(jù)各個(gè)映射的關(guān)系,利用迭代法構(gòu)造奇偶點(diǎn)列,得出了:|| Sx-Ty,c1,…,cn-1 ||≤f(||x-y,c1,…,cn-1 ||)||x-y,c1,…,cn-1 ||f(t)為[0,+∞)到[0,1)內(nèi)的函數(shù),利用弱相容自映射的性質(zhì),證明了多個(gè)壓縮映射的公共不動(dòng)點(diǎn)定理.
[Abstract]:The fixed point theory is actually the solution of operator equation TX = x, which is the theoretical basis for solving the existence and uniqueness of the solutions of many algebraic equations, integral equations and differential equations, and is one of the important contents in functional analysis.In this paper, the convergence sequences on n-Banach spaces are constructed by iterative method, and the existence and uniqueness of fixed points of contractive mappings in n-Banach spaces are proved, which generalizes and improves some conclusions in the literature. The main results obtained are as follows: 1.In n-Banach space, we generalize the constant 胃 in [0, 鈭，

本文編號(hào)：1762588