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Paper   IPM / M / 520
School of Mathematics
  Title:   Asymptotic properties of nonexpansive iterations in reflexive spaces
1.  B. Djafari Rouhani
2.  W. A. Kirk
  Status:   Published
  Journal: J. Math. Anal. Appl.
  No.:  2
  Vol.:  236
  Year:  1999
  Pages:   281-289
  Supported by:  IPM
Let X be a reflexive Banach space and (xn)n ≥ 0 a nonexpansive (resp., firmly nonexpansive) sequence in X. It is shown that the set of weak ω-limit points of the sequence (xn/n)n ≥ 1 (resp., (xn+1xn)n ≥ 0) always lies on a convex subset of a sphere centered at the origin of radius d=limn→ ∞|| xn/n||. This fact quickly yields previous results of B. Djafari Rouhani as well as recent results of J.S. Jung and J.S. Park. Potential applications are also discussed.

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