Accelerated modified inertial Mann and viscosity algorithms to find a fixed point of $ \alpha - $inverse strongly monotone operators

Hasanen A. Hammad; Habib ur Rehman; Manuel De la Sen; Hasanen A. Hammad; Habib ur Rehman; Manuel De la Sen

doi:10.3934/math.2021522

AIMS Mathematics

2021, Volume 6, Issue 8: 9000-9019. doi: 10.3934/math.2021522

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Research article

Accelerated modified inertial Mann and viscosity algorithms to find a fixed point of $ \alpha - $inverse strongly monotone operators

1.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
2.
Department of Mathematics, Monglkuts University of Technology, Bangkok 10140, Thailand
3.
Institute of Research and Development of Processes University of the Basque Country 48940- Leioa (Bizkaia), Spain

Received: 23 April 2021 Accepted: 11 June 2021 Published: 16 June 2021
MSC : 47H06, 47H09, 47J25

In this paper, strong convergence results for $ \alpha - $inverse strongly monotone operators under new algorithms in the framework of Hilbert spaces are discussed. Our algorithms are the combination of the inertial Mann forward-backward method with the CQ-shrinking projection method and viscosity algorithm. Our methods lead to an acceleration of modified inertial Mann Halpern and viscosity algorithms. Later on, numerical examples to illustrate the applications, performance, and effectiveness of our algorithms are presented.
- inertial Mann forward-backward method,
- strong convergence theorems,
- viscosity algorithm,
- CQ-projection method,
- shrinking projection method
Citation: Hasanen A. Hammad, Habib ur Rehman, Manuel De la Sen. Accelerated modified inertial Mann and viscosity algorithms to find a fixed point of $ \alpha - $inverse strongly monotone operators[J]. AIMS Mathematics, 2021, 6(8): 9000-9019. doi: 10.3934/math.2021522

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Abstract

In this paper, strong convergence results for $ \alpha - $inverse strongly monotone operators under new algorithms in the framework of Hilbert spaces are discussed. Our algorithms are the combination of the inertial Mann forward-backward method with the CQ-shrinking projection method and viscosity algorithm. Our methods lead to an acceleration of modified inertial Mann Halpern and viscosity algorithms. Later on, numerical examples to illustrate the applications, performance, and effectiveness of our algorithms are presented.

References

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