n-Banach空间中压缩映射不动点理论

发布时间：2018-04-17 07:10

  本文选题：n-Banach空间 + 压缩映射　； 参考：《西北大学》2017年硕士论文

【摘要】：不动点理论实际是算子方程Tx = x的求解问题,是解决许多代数方程,积分方程,微分方程解的存在唯一性的理论基础,是泛函分析中的重要内容之一.本文利用迭代法,构造n-Banach空间上的收敛序列,证明了n-Banach空间中压缩映射不动点的存在性和唯一性,从而推广和改进了文献中的一些结论,所取得的主要成果如下:1.在n-Banach空间中,将经典压缩的映射ρ(Tx,Ty)≤θρ(x,y),θ∈[0,1)中常数θ推广为[0,+∞)到[0,1)内的一元函数f(t),得出了:|| Tx-Ty,c1,…,Cn-1 ||≤ f(||x-y,c1,…,cn-1||)|| x-y,c1,…,cn-1 ||从而证明了的几类不同压缩映射的不动点定理.2.在n-Banach空间中,根据各个映射的关系,利用迭代法构造奇偶点列,得出了:|| Sx-Ty,c1,…,cn-1 ||≤f(||x-y,c1,…,cn-1 ||)||x-y,c1,…,cn-1 ||f(t)为[0,+∞)到[0,1)内的函数,利用弱相容自映射的性质,证明了多个压缩映射的公共不动点定理.
[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，

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