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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 97
   School of Mathematics
  Title: On the extension of families of nonlinear operators having a common fixed point
  Author(s): B. Djafari Rouhani
  Status: Published
  Journal: Math. Sci. Res. Hot-Line
  No.: 2
  Vol.: 3
  Year: 1999
  Pages: 1-10
  Supported by: IPM
  Abstract:
Let D be a nonempty subset of a real Banach space X. A sequence (Tn)n ≥ 0 of self maps of D is called almost asymptotically nonexpansive if there exist sequences {kn} and {εn} of positive numbers with limn→∞ kn=1 and limn→ ∞ εn=0 such that
|| Ti+lxTj+ly||2kl2||TixTjy||2+ εl2  for  all i,j,l ≥ 0
and all x,y in D.
First, in a Hilbert space, we show the existence of an extension to such a sequence of self maps of D with a common fixed point.
A self map T of D is called symptotically nonexpansive if there exists a sequence {kn} of positive numbers with limn→ ∞ kn=1 such that ||Tn xTn y|| ≤ kn|| xy|| for all n ≥ 0 and x,y in D. by introducing the notions of absolute and almost absolute fixed points for T, we investigate the existence of such points for such mappings in a Hilbert space.

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