Approximations of fixed points in the Hadamard metric space CATp(0)

Mostafa Bachar; Mohamed Amine Khamsi

doi:10.3390/math7111088

Approximations of fixed points in the Hadamard metric space CAT_p(0)

Mostafa Bachar, Mohamed Amine Khamsi

Mathematics

College of Sciences

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

4 Scopus citations

Abstract

In this paper, we consider the recently introduced CAT_p(0), where the comparison triangles belong to l_p, for p ≥ 2. We first establish an inequality in these nonlinear metric spaces. Then, we use it to prove the existence of fixed points of asymptotically nonexpansive mappings defined in CAT_p(0). Moreover, we discuss the behavior of the successive iteration introduced by Schu for these mappings in Banach spaces. In particular, we prove that the successive iteration generates an approximate fixed point sequence.

Original language	British English
Article number	1088
Journal	Mathematics
Volume	7
Issue number	11
DOIs	https://doi.org/10.3390/math7111088
State	Published - 1 Nov 2019

Keywords

Fixed point
Generalized CAT(0) spaces
Hadamard metric spaces
Hyperbolic metric spaces
Lipschitzian mapping
Modified Mann iteration

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10.3390/math7111088

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title = "Approximations of fixed points in the Hadamard metric space CATp(0)",

abstract = "In this paper, we consider the recently introduced CATp(0), where the comparison triangles belong to lp, for p ≥ 2. We first establish an inequality in these nonlinear metric spaces. Then, we use it to prove the existence of fixed points of asymptotically nonexpansive mappings defined in CATp(0). Moreover, we discuss the behavior of the successive iteration introduced by Schu for these mappings in Banach spaces. In particular, we prove that the successive iteration generates an approximate fixed point sequence.",

keywords = "Fixed point, Generalized CAT(0) spaces, Hadamard metric spaces, Hyperbolic metric spaces, Lipschitzian mapping, Modified Mann iteration",

author = "Mostafa Bachar and Khamsi, {Mohamed Amine}",

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AU - Khamsi, Mohamed Amine

N1 - Funding Information: The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for funding this research group No. (RG-1435-079). Deanship of Scientific Research at King Saud University, research group No. (RG-1435-079). Publisher Copyright: © 2019 by the authors.

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N2 - In this paper, we consider the recently introduced CATp(0), where the comparison triangles belong to lp, for p ≥ 2. We first establish an inequality in these nonlinear metric spaces. Then, we use it to prove the existence of fixed points of asymptotically nonexpansive mappings defined in CATp(0). Moreover, we discuss the behavior of the successive iteration introduced by Schu for these mappings in Banach spaces. In particular, we prove that the successive iteration generates an approximate fixed point sequence.

AB - In this paper, we consider the recently introduced CATp(0), where the comparison triangles belong to lp, for p ≥ 2. We first establish an inequality in these nonlinear metric spaces. Then, we use it to prove the existence of fixed points of asymptotically nonexpansive mappings defined in CATp(0). Moreover, we discuss the behavior of the successive iteration introduced by Schu for these mappings in Banach spaces. In particular, we prove that the successive iteration generates an approximate fixed point sequence.

KW - Fixed point

KW - Generalized CAT(0) spaces

KW - Hadamard metric spaces

KW - Hyperbolic metric spaces

KW - Lipschitzian mapping

KW - Modified Mann iteration

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VL - 7

JO - Mathematics

JF - Mathematics

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ER -

Approximations of fixed points in the Hadamard metric space CAT_p(0)

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Keywords

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