A Subgradient-Type Extrapolation Cyclic Method for Solving an Equilibrium Problem over the Common Fixed-Point Sets

In this paper, we consider the solving of an equilibrium problem over the common fixed set of cutter mappings in a real Hilbert space. To this end, we present a subgradient-type extrapolation cyclic method. The proposed method is generated based on the ideas of a subgradient method and an extrapolat...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-05, Vol.14 (5), p.992
Main Authors: Promsinchai, Porntip, Nimana, Nimit
Format: Article
Language:English
Subjects:
Algorithms
Convergence
convergence analysis
cutter
Equilibrium
equilibrium problem
Extrapolation
fixed point
Hilbert space
Methods
monotone operator
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Summary:In this paper, we consider the solving of an equilibrium problem over the common fixed set of cutter mappings in a real Hilbert space. To this end, we present a subgradient-type extrapolation cyclic method. The proposed method is generated based on the ideas of a subgradient method and an extrapolated cyclic cutter method. We prove a strong convergence of the method provided that some suitable assumptions of step-size sequences are assumed. We finally show the numerical behavior of the proposed method.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14050992