Approximate fixed point sequences of nonlinear semigroups in metric spaces

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Abstract

In this paper, we investigate the common approximate fixed point sequences of nonexpan-sive semigroups of nonlinear mappings {Tt}t≥0, i.e., a family such that T0(x) = x, Ts+t = Ts(Tt(x)), where the domain is a metric space (M, d). In particular, we prove that under suitable conditions the common approximate fixed point sequences set is the same as the common approximate fixed point sequences set of two mappings from the family. Then we use the Ishikawa iteration to construct a common approximate fixed point sequence of nonexpansive semigroups of nonlinear mappings.

Original languageBritish English
Pages (from-to)297-305
Number of pages9
JournalCanadian Mathematical Bulletin
Volume58
Issue number2
DOIs
StatePublished - Jun 2015

Keywords

  • Approximate fixed point
  • Fixed point
  • Hyperbolic metric space
  • Ishikawa iterations
  • Nonexpansive mapping
  • Semigroup of mappings
  • Uniformly convex hyperbolic space

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