Approximate Fixed Point Sequences of Nonlinear Semigroups in Metric Spaces
Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 297-305
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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.
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
Khamsi, M. A. Approximate Fixed Point Sequences of Nonlinear Semigroups in Metric Spaces. Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 297-305. doi: 10.4153/CMB-2014-026-x
@article{10_4153_CMB_2014_026_x,
author = {Khamsi, M. A.},
title = {Approximate {Fixed} {Point} {Sequences} of {Nonlinear} {Semigroups} in {Metric} {Spaces}},
journal = {Canadian mathematical bulletin},
pages = {297--305},
year = {2015},
volume = {58},
number = {2},
doi = {10.4153/CMB-2014-026-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-026-x/}
}
TY - JOUR AU - Khamsi, M. A. TI - Approximate Fixed Point Sequences of Nonlinear Semigroups in Metric Spaces JO - Canadian mathematical bulletin PY - 2015 SP - 297 EP - 305 VL - 58 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-026-x/ DO - 10.4153/CMB-2014-026-x ID - 10_4153_CMB_2014_026_x ER -
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