Approximate fixed point sequences of nonlinear semigroups in metric spaces

M. A. Khamsi

doi:10.4153/CMB-2014-026-x

Approximate fixed point sequences of nonlinear semigroups in metric spaces

M. A. Khamsi^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we investigate the common approximate fixed point sequences of nonexpan-sive semigroups of nonlinear mappings {T_t}_t≥0, i.e., a family such that T₀(x) = x, T_s+t = T_s(T_t(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 language	English
Pages (from-to)	297-305
Number of pages	9
Journal	Canadian Mathematical Bulletin
Volume	58
Issue number	2
DOIs	https://doi.org/10.4153/CMB-2014-026-x
State	Published - Jun 2015

Bibliographical note

Publisher Copyright:
© Canadian Mathematical Society 2015.

Keywords

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

ASJC Scopus subject areas

General Mathematics

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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.",

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PY - 2015/6

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N2 - 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.

AB - 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.

KW - Approximate fixed point

KW - Fixed point

KW - Hyperbolic metric space

KW - Ishikawa iterations

KW - Nonexpansive mapping

KW - Semigroup of mappings

KW - Uniformly convex hyperbolic space

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DO - 10.4153/CMB-2014-026-x

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AN - SCOPUS:84978977109

SN - 0008-4395

VL - 58

SP - 297

EP - 305

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 2

ER -

Approximate fixed point sequences of nonlinear semigroups in metric spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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