Taiwanese Journal of Mathematics

NONLINEAR MEAN ERGODIC THEOREMS

Isao Miyadera

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Abstract

Let $C$ be a nonempty subset (not necessarily closed and convex) of a Hilbert space, and $T: C \rightarrow C$ be a nonlinear mapping (not necessarily asymptotically nonexpansive). In this paper, we study the convergence of $(1/n)\sum^{n-1}_{i=0} T^i x(x\in C)$ as $n \rightarrow \infty $.

Article information

Source
Taiwanese J. Math., Volume 1, Number 4 (1997), 433-449.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406121

Digital Object Identifier
doi:10.11650/twjm/1500406121

Mathematical Reviews number (MathSciNet)
MR1486564

Zentralblatt MATH identifier
0912.47029

Subjects
Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Keywords
nonlinear ergodic theorem fixed point nonexpansive mapping weak almost-convergence strong almost-convergence asymptotic center asymptotically nonexpansive mapping asymptotically nonexpansive mapping in the intermediate sense

Citation

Miyadera, Isao. NONLINEAR MEAN ERGODIC THEOREMS. Taiwanese J. Math. 1 (1997), no. 4, 433--449. doi:10.11650/twjm/1500406121. https://projecteuclid.org/euclid.twjm/1500406121


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