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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
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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