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

Francis Akutsah; Akindele Adebayo Mebawondu; Austine Efut Ofem; Reny George; Hossam A. Nabwey; Ojen Kumar Narain; Francis Akutsah; Akindele Adebayo Mebawondu; Austine Efut Ofem; Reny George; Hossam A. Nabwey; Ojen Kumar Narain

doi:10.3934/math.2024839

AIMS Mathematics

2024, Volume 9, Issue 7: 17276-17290. doi: 10.3934/math.2024839

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

1.
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
2.
Mountain Top University, Prayer City, Ogun State Nigeria
3.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
4.
Department of Basic Engineering, Faculty of Engineering, Menoufia University, Shibin el Kom 32511, Egypt

Received: 06 March 2024 Revised: 28 April 2024 Accepted: 09 May 2024 Published: 20 May 2024
MSC : 26A33, 34B10, 34B15

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.
- subgradient extragradient,
- mildly inertial,
- equilibrium problem,
- fixed point problem
Citation: Francis Akutsah, Akindele Adebayo Mebawondu, Austine Efut Ofem, Reny George, Hossam A. Nabwey, Ojen Kumar Narain. Modified mildly inertial subgradient extragradient method for solving pseudomonotone equilibrium problems and nonexpansive fixed point problems[J]. AIMS Mathematics, 2024, 9(7): 17276-17290. doi: 10.3934/math.2024839

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Abstract

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.

References

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