TY - JOUR

T1 - A self-adaptive inertial subgradient extragradient method for pseudomonotone equilibrium and common fixed point problems

AU - Jolaoso, Lateef Olakunle

AU - Aphane, Maggie

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.
Funding Information:
This first author is supported by the postdoctoral research grant from the Sefako Makgatho Health Sciences University, South Africa. Acknowledgements Availability of data and materials
Publisher Copyright:
© 2020, The Author(s).

PY - 2020/12/1

Y1 - 2020/12/1

N2 - In this paper, we introduce a self-adaptive inertial subgradient extragradient method for solving pseudomonotone equilibrium problem and common fixed point problem in real Hilbert spaces. The algorithm consists of an inertial extrapolation process for speeding the rate of its convergence, a monotone nonincreasing stepsize rule, and a viscosity approximation method which guaranteed its strong convergence. More so, a strong convergence theorem is proved for the sequence generated by the algorithm under some mild conditions and without prior knowledge of the Lipschitz-like constants of the equilibrium bifunction. We further provide some numerical examples to illustrate the performance and accuracy of our method.

AB - In this paper, we introduce a self-adaptive inertial subgradient extragradient method for solving pseudomonotone equilibrium problem and common fixed point problem in real Hilbert spaces. The algorithm consists of an inertial extrapolation process for speeding the rate of its convergence, a monotone nonincreasing stepsize rule, and a viscosity approximation method which guaranteed its strong convergence. More so, a strong convergence theorem is proved for the sequence generated by the algorithm under some mild conditions and without prior knowledge of the Lipschitz-like constants of the equilibrium bifunction. We further provide some numerical examples to illustrate the performance and accuracy of our method.

KW - Common fixed point

KW - Equilibrium problems

KW - Extragradient method

KW - Pseudomonotone

KW - Self-adaptive method

UR - http://www.scopus.com/inward/record.url?scp=85087383178&partnerID=8YFLogxK

U2 - 10.1186/s13663-020-00676-y

DO - 10.1186/s13663-020-00676-y

M3 - Article

AN - SCOPUS:85087383178

VL - 2020

JO - Fixed Point Theory and Applications

JF - Fixed Point Theory and Applications

SN - 1687-1820

IS - 1

M1 - 9

ER -