Approximate Fixed Point Sequences of Nonlinear Semigroups in Metric Spaces

Khamsi, M. A.

Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 297-305

Résumé

In this paper, we investigate the common approximate fixed point sequences of nonexpansive semigroups of nonlinear mappings ${{\left\{ {{T}_{t}} \right\}}_{t\ge 0}}$ , i.e., a family such that ${{T}_{0}}\left( x \right)\,=\,x,\,{{T}_{s+t}}\,=\,{{T}_{s}}\left( {{T}_{t}}\left( x \right) \right)$ , where the domain is a metric space $\left( M,\,d \right)$ . 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.

Détail

DOI : 10.4153/CMB-2014-026-x

Mots-clés : 47H09, 46B20, 47H10, 47E10, approximate fixed point, fixed point, hyperbolic metric space, Ishikawa iterations, nonexpansive mapping, semigroup of mappings, uniformly convex hyperbolic space

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