Iterative Solutions of Nonlinear Equations of the Strongly Accretive Type

Let E be a real q-uniformly smooth Banach space. Suppose T is a strongly pseudo-contractive map with open domain D(T) in E. Suppose further that T has a fixed point in D(T). Under various continuity assumptions on T it is proved that each of the Mann iteration process or the Ishikawa iteration method converges strongly to the unique fixed point of T. Related results deal with iterative solutions of nonlinear operator equations involving strongly accretive maps. Explicit error estimates are also provided.     

Convergence theorems of fixed points for Lipschitz pseudo-contractions in Hilbert spaces

Let C be a closed convex subset of a real Hilbert space H and assume that T is a κ-strict pseudo-contraction on C. Consider Mann's iteration algorithm given by

     

Hilbert空间中Lipschitz单调映像变分不等式解的另一个逼近定理

首先给出了Hilbert空间中Lipschitz单调映像变分不等式解的迭代格式,并证明了其收敛性.作为应用,证明了Hilbert空间中Lipschitz伪压缩映像的强收敛定理,扩展了已知的相关结果.     

Banach空间中关于变分不等式组与严格伪压缩映射的广义迭代法(英文)

本文利用广义迭代法建立一迭代序列,通过该序列讨论Banach空间中一类广义变分不等式组的解与有限个严格伪压缩映射的公共不动点,并且得到该序列的强收敛性.本文所得结论推广和提高了以前一些相应结果.     

Banach空间中渐近非扩张映象不动点的迭代逼近问题

本文研究Banach空间中渐近非扩张映象和渐近伪压缩映象不动点的迭代逼近问题,本文结果是[4,5,7]中相应结果的发展和改进。     

Iterative approximation of the solution of a locally Lipschitzian equation

Suppose X=L_p,(or l_p),p>2.T:D(T)→X is a locally Lipschitzian and strictlyaccretive operator.In this paper.the iterative approximation of the solution of nonlinearequation Tx=y is given and the iterative approximation of a fixed point of a locallyLipschitzian and strictly pseudo-contractive mapping is discussed.