Modified mildly inertial subgradient extragradient method for solving pseudomonotone equilibrium problems and nonexpansive fixed point problems

This paper presents and examines a newly improved linear technique for solving the equilibrium problem of a pseudomonotone operator and the fixed point problem of a nonexpansive mapping within a real Hilbert space framework. The technique relies two modified mildly inertial methods and the subgradie...

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Published inAIMS mathematics Vol. 9; no. 7; pp. 17276 - 17290
Main Authors Akutsah, Francis, Mebawondu, Akindele Adebayo, Ofem, Austine Efut, George, Reny, Nabwey, Hossam A., Narain, Ojen Kumar
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
equilibrium problem
fixed point problem
mildly inertial
subgradient extragradient
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Summary:This paper presents and examines a newly improved linear technique for solving the equilibrium problem of a pseudomonotone operator and the fixed point problem of a nonexpansive mapping within a real Hilbert space framework. The technique relies two modified mildly inertial methods and the subgradient extragradient approach. In addition, it can be viewed as an advancement over the previously known inertial subgradient extragradient approach. Based on common assumptions, the algorithm's weak convergence has been established. Finally, in order to confirm the efficiency and benefit of the proposed algorithm, we present a few numerical experiments.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024839