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

Fixexd point theory and applications

article

Jolaoso, Lateef Olakunle¹  Aphane, Maggie¹ 

[1] Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University

关键词: Extragradient method;    Equilibrium problems;    Common fixed point;    Self-adaptive method;    Pseudomonotone;   

DOI  :  10.1186/s13663-020-00676-y

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

Unknown