Split variational inclusion problem and fixed point problem for a class of multivalued mappings in CAT(0) spaces

Mujahid Abbas; Yusuf Ibrahim; Abdul Rahim Khan; Manuel De la Sen

doi:10.3390/math7080749

Split variational inclusion problem and fixed point problem for a class of multivalued mappings in CAT(0) spaces

Mujahid Abbas
, Yusuf Ibrahim
, Abdul Rahim Khan
, Manuel De la Sen

Government College University Lahore
University of Pretoria
Sa'adatu Rimi College of Education
King Fahd University of Petroleum and Minerals
University of the Basque Country

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

10 Citations (Scopus)

Abstract

The aim of this paper is to introduce a modified viscosity iterative method to approximate a solution of the split variational inclusion problem and fixed point problem for a uniformly continuous multivalued total asymptotically strictly pseudocontractive mapping in CAT(0) spaces. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. Furthermore, we solve a split Hammerstein integral inclusion problem and fixed point problem as an application to validate our result. It seems that our main result in the split variational inclusion problem is new in the setting of CAT(0) spaces.

Original language	English
Article number	749
Journal	Mathematics
Volume	7
Issue number	8
DOIs	https://doi.org/10.3390/math7080749
Publication status	Published - 1 Aug 2019
Externally published	Yes

Keywords

CAT(0) space
Fixed point problem
Split variational inclusion problem
Total asymptotically strictly pseudocontractive mapping

ASJC Scopus subject areas

General Mathematics

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10.3390/math7080749

Cite this

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title = "Split variational inclusion problem and fixed point problem for a class of multivalued mappings in CAT(0) spaces",

abstract = "The aim of this paper is to introduce a modified viscosity iterative method to approximate a solution of the split variational inclusion problem and fixed point problem for a uniformly continuous multivalued total asymptotically strictly pseudocontractive mapping in CAT(0) spaces. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. Furthermore, we solve a split Hammerstein integral inclusion problem and fixed point problem as an application to validate our result. It seems that our main result in the split variational inclusion problem is new in the setting of CAT(0) spaces.",

keywords = "CAT(0) space, Fixed point problem, Split variational inclusion problem, Total asymptotically strictly pseudocontractive mapping",

author = "Mujahid Abbas and Yusuf Ibrahim and Khan, \{Abdul Rahim\} and \{De la Sen\}, Manuel",

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AU - Abbas, Mujahid

AU - Ibrahim, Yusuf

AU - Khan, Abdul Rahim

AU - De la Sen, Manuel

PY - 2019/8/1

Y1 - 2019/8/1

N2 - The aim of this paper is to introduce a modified viscosity iterative method to approximate a solution of the split variational inclusion problem and fixed point problem for a uniformly continuous multivalued total asymptotically strictly pseudocontractive mapping in CAT(0) spaces. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. Furthermore, we solve a split Hammerstein integral inclusion problem and fixed point problem as an application to validate our result. It seems that our main result in the split variational inclusion problem is new in the setting of CAT(0) spaces.

AB - The aim of this paper is to introduce a modified viscosity iterative method to approximate a solution of the split variational inclusion problem and fixed point problem for a uniformly continuous multivalued total asymptotically strictly pseudocontractive mapping in CAT(0) spaces. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. Furthermore, we solve a split Hammerstein integral inclusion problem and fixed point problem as an application to validate our result. It seems that our main result in the split variational inclusion problem is new in the setting of CAT(0) spaces.

KW - CAT(0) space

KW - Fixed point problem

KW - Split variational inclusion problem

KW - Total asymptotically strictly pseudocontractive mapping

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DO - 10.3390/math7080749

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SN - 2227-7390

VL - 7

JO - Mathematics

JF - Mathematics

IS - 8

M1 - 749

ER -

Split variational inclusion problem and fixed point problem for a class of multivalued mappings in CAT(0) spaces

Abstract

Keywords

ASJC Scopus subject areas

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