A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
作者： Ronald E. Bruck
DOI: 10.1007/BF02764907
关键词: Discrete mathematics 、 Banach space 、 Closed graph theorem 、 Uniform boundedness principle 、 Bounded inverse theorem 、 Banach–Mazur theorem 、 Mathematics 、 Pure mathematics 、 Eberlein–Šmulian theorem 、 Open mapping theorem (functional analysis) 、 Inverse function theorem
摘要: The following theorem is proven:if E a uniformly rotund Banach space with Frechet differentiable norm, C bounded nonempty closed convex subset of E, and T: C→C contraction, then the iterates {Tnx} are weakly almost-convergent to fixed-point T.
springer.com
sci-hub.se 参考文章(5)
Felix E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces ,(1976)
G. G. Lorentz, A contribution to the theory of divergent sequences Acta Mathematica. ,vol. 80, pp. 167- 190 ,(1948) , 10.1007/BF02393648
Ronald E. Bruck, On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak ω-limit set Israel Journal of Mathematics. ,vol. 29, pp. 1- 16 ,(1978) , 10.1007/BF02760397
Ralph DeMarr, Common fixed points for commuting contraction mappings Pacific Journal of Mathematics. ,vol. 13, pp. 1139- 1141 ,(1963) , 10.2140/PJM.1963.13.1139
Felix Browder, Nonlinear Operators and Nonlinear Equations of Evolution American Mathematical Society. ,(1976) , 10.1090/PSPUM/018.2