Generalized implicit viscosity approximation method for multivalued mappings in CAT(0) spaces

Mujahid Abbas; Hira Iqbal; Manuel De La Sen

doi:10.1515/dema-2019-0031

Generalized implicit viscosity approximation method for multivalued mappings in CAT(0) spaces

Mujahid Abbas, Hira Iqbal, Manuel De La Sen

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

Abstract

We prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space. Under certain appropriate conditions on parameters, we show that such a sequence converges strongly to a fixed point of the mapping which solves a variational inequality. We also present some convergence results for the implicit viscosity approximation method in complete-trees without the endpoint condition.

Original language	English
Pages (from-to)	347-360
Number of pages	14
Journal	Demonstratio Mathematica
Volume	52
Issue number	1
DOIs	https://doi.org/10.1515/dema-2019-0031
Publication status	Published - 1 Jan 2019
Externally published	Yes

Keywords

CAT(0) space
multivalued nonexpansive mapping
variational inequality
viscosity approximation method

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1515/dema-2019-0031

Cite this

@article{27a6a1904f754d0182d6ae9b606f0d49,

title = "Generalized implicit viscosity approximation method for multivalued mappings in CAT(0) spaces",

abstract = "We prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space. Under certain appropriate conditions on parameters, we show that such a sequence converges strongly to a fixed point of the mapping which solves a variational inequality. We also present some convergence results for the implicit viscosity approximation method in complete-trees without the endpoint condition.",

keywords = "CAT(0) space, multivalued nonexpansive mapping, variational inequality, viscosity approximation method",

author = "Mujahid Abbas and Hira Iqbal and \{De La Sen\}, Manuel",

note = "Publisher Copyright: {\textcopyright} 2019 Mujahid Abbas et al., published by De Gruyter Open.",

year = "2019",

month = jan,

day = "1",

doi = "10.1515/dema-2019-0031",

language = "English",

volume = "52",

pages = "347--360",

journal = "Demonstratio Mathematica",

issn = "0420-1213",

publisher = "Walter de Gruyter GmbH",

number = "1",

}

TY - JOUR

T1 - Generalized implicit viscosity approximation method for multivalued mappings in CAT(0) spaces

AU - Abbas, Mujahid

AU - Iqbal, Hira

AU - De La Sen, Manuel

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space. Under certain appropriate conditions on parameters, we show that such a sequence converges strongly to a fixed point of the mapping which solves a variational inequality. We also present some convergence results for the implicit viscosity approximation method in complete-trees without the endpoint condition.

AB - We prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space. Under certain appropriate conditions on parameters, we show that such a sequence converges strongly to a fixed point of the mapping which solves a variational inequality. We also present some convergence results for the implicit viscosity approximation method in complete-trees without the endpoint condition.

KW - CAT(0) space

KW - multivalued nonexpansive mapping

KW - variational inequality

KW - viscosity approximation method

UR - https://www.scopus.com/pages/publications/85079271829

U2 - 10.1515/dema-2019-0031

DO - 10.1515/dema-2019-0031

M3 - Article

AN - SCOPUS:85079271829

SN - 0420-1213

VL - 52

SP - 347

EP - 360

JO - Demonstratio Mathematica

JF - Demonstratio Mathematica

IS - 1

ER -

Generalized implicit viscosity approximation method for multivalued mappings in CAT(0) spaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this