TY - JOUR

T1 - A parallel viscosity extragradient method for solving a system of pseudomonotone equilibrium problems and fixed point problems in Hadamard spaces

AU - Aremu, Kazeem Olalekan

AU - Jolaoso, Lateef Olakunle

AU - Aphane, Maggie

AU - Oyewole, Olawale Kazeem

N1 - Funding Information:
The authors acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University for making their facilities available for the research. O.K. Oyewole acknowledges with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF COE-MaSS) Doctoral Bursary.
Funding Information:
L.O. Jolaoso is supported by the Postdoctoral research grant from the Sefako Makgatho Health Sciences University, South Africa.
Publisher Copyright:
© 2021, Università degli Studi di Napoli "Federico II".

PY - 2021

Y1 - 2021

N2 - In this work, we study a parallel viscosity extragradient method for approximating a common solution of a finite system of pseudomonotone equilibrium problems and common fixed point problem for nonexpansive mappings in Hadamard spaces. We propose an iterative method and prove its strong convergence to an element in the intersection of the solution set of finite system of equilibrium problems and the fixed points set of nonexpansive mappings. Furthermore, we give an example in a Hadamard space which is not an Hilbert space to support the convergence theorem in the paper. This result generalizes and extends recent results in the literature.

AB - In this work, we study a parallel viscosity extragradient method for approximating a common solution of a finite system of pseudomonotone equilibrium problems and common fixed point problem for nonexpansive mappings in Hadamard spaces. We propose an iterative method and prove its strong convergence to an element in the intersection of the solution set of finite system of equilibrium problems and the fixed points set of nonexpansive mappings. Furthermore, we give an example in a Hadamard space which is not an Hilbert space to support the convergence theorem in the paper. This result generalizes and extends recent results in the literature.

KW - Common fixed point

KW - Equilibrium problems

KW - Extragradient method

KW - Hadamard spaces

KW - Pseudomontone

UR - http://www.scopus.com/inward/record.url?scp=85114100116&partnerID=8YFLogxK

U2 - 10.1007/s11587-021-00640-x

DO - 10.1007/s11587-021-00640-x

M3 - Article

AN - SCOPUS:85114100116

JO - Ricerche di Matematica

JF - Ricerche di Matematica

SN - 0035-5038

ER -