Kirk type iteration process and convex feasibility problem in CAT(0) space

A. R. Khan; H. Fukhar-ud-din; D. M. Oyetunbi

doi:10.1007/s13370-020-00843-9

Kirk type iteration process and convex feasibility problem in CAT(0) space

A. R. Khan^*
, H. Fukhar-ud-din
, D. M. Oyetunbi

^*Corresponding author for this work

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

Abstract

In this paper, we establish △ -convergence and strong convergence of Kirk type iteration process in CAT(0) spaces. We apply our results to solve consistent and inconsistent convex feasibility problems in CAT(0) spaces. This work improves and extends the corresponding results of Kirk, Kuhfittig, Rhoades and Takahashi and Tamura on a nonlinear domain.

Original language	English
Pages (from-to)	543-554
Number of pages	12
Journal	Afrika Matematika
Volume	32
Issue number	3-4
DOIs	https://doi.org/10.1007/s13370-020-00843-9
State	Published - Jun 2021

Bibliographical note

Publisher Copyright:
© 2020, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.

Keywords

CAT(0) space
Convex combination
Feasibility problem
Image recovery
Kirk process
Nonexpansive mapping
▵-Convergence and strong convergence

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s13370-020-00843-9

Cite this

@article{6b49fa8f01564ab8b159596b63a5e9b2,

title = "Kirk type iteration process and convex feasibility problem in CAT(0) space",

abstract = "In this paper, we establish △ -convergence and strong convergence of Kirk type iteration process in CAT(0) spaces. We apply our results to solve consistent and inconsistent convex feasibility problems in CAT(0) spaces. This work improves and extends the corresponding results of Kirk, Kuhfittig, Rhoades and Takahashi and Tamura on a nonlinear domain.",

keywords = "CAT(0) space, Convex combination, Feasibility problem, Image recovery, Kirk process, Nonexpansive mapping, ▵-Convergence and strong convergence",

author = "Khan, \{A. R.\} and H. Fukhar-ud-din and Oyetunbi, \{D. M.\}",

note = "Publisher Copyright: {\textcopyright} 2020, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.",

year = "2021",

month = jun,

doi = "10.1007/s13370-020-00843-9",

language = "English",

volume = "32",

pages = "543--554",

journal = "Afrika Matematika",

issn = "1012-9405",

publisher = "Springer Science + Business Media",

number = "3-4",

}

TY - JOUR

T1 - Kirk type iteration process and convex feasibility problem in CAT(0) space

AU - Khan, A. R.

AU - Fukhar-ud-din, H.

AU - Oyetunbi, D. M.

PY - 2021/6

Y1 - 2021/6

N2 - In this paper, we establish △ -convergence and strong convergence of Kirk type iteration process in CAT(0) spaces. We apply our results to solve consistent and inconsistent convex feasibility problems in CAT(0) spaces. This work improves and extends the corresponding results of Kirk, Kuhfittig, Rhoades and Takahashi and Tamura on a nonlinear domain.

AB - In this paper, we establish △ -convergence and strong convergence of Kirk type iteration process in CAT(0) spaces. We apply our results to solve consistent and inconsistent convex feasibility problems in CAT(0) spaces. This work improves and extends the corresponding results of Kirk, Kuhfittig, Rhoades and Takahashi and Tamura on a nonlinear domain.

KW - CAT(0) space

KW - Convex combination

KW - Feasibility problem

KW - Image recovery

KW - Kirk process

KW - Nonexpansive mapping

KW - ▵-Convergence and strong convergence

UR - https://www.scopus.com/pages/publications/85091786520

U2 - 10.1007/s13370-020-00843-9

DO - 10.1007/s13370-020-00843-9

M3 - Article

AN - SCOPUS:85091786520

SN - 1012-9405

VL - 32

SP - 543

EP - 554

JO - Afrika Matematika

JF - Afrika Matematika

IS - 3-4

ER -

Kirk type iteration process and convex feasibility problem in CAT(0) space

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this