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

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...

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Bibliographic Details
Published in:Fixed point theory and applications (Hindawi Publishing Corporation) 2020-07, Vol.2020 (1), p.1-22, Article 9
Main Authors: Jolaoso, Lateef Olakunle, Aphane, Maggie
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Common fixed point
Differential Geometry
Equilibrium problems
Extragradient method
Iterative Methods and Optimization Algorithms: A Dedication to Dr. Hong-Kun Xu
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Pseudomonotone
Self-adaptive method
Topology
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Summary: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.
ISSN:1687-1812
1687-1812
DOI:10.1186/s13663-020-00676-y