Modified Tseng's splitting algorithms for the sum of two monotone operators in Banach spaces

Jun Yang; Prasit Cholamjiak; Pongsakorn Sunthrayuth; Jun Yang; Prasit Cholamjiak; Pongsakorn Sunthrayuth

doi:10.3934/math.2021286

AIMS Mathematics

2021, Volume 6, Issue 5: 4873-4900. doi: 10.3934/math.2021286

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Research article

Modified Tseng's splitting algorithms for the sum of two monotone operators in Banach spaces

1.
School of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, Shaanxi, China
2.
School of Science, University of Phayao, Phayao 56000, Thailand
3.
Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, Thailand

Received: 28 December 2020 Accepted: 25 February 2021 Published: 01 March 2021
MSC : 47H09, 47H10, 47J25

In this work, we introduce two modified Tseng's splitting algorithms with a new non-monotone adaptive step size for solving monotone inclusion problem in the framework of Banach spaces. Under some mild assumptions, we establish the weak and strong convergence results of the proposed algorithms. Moreover, we also apply our results to variational inequality problem, convex minimization problem and signal recovery, and provide several numerical experiments including comparisons with other related algorithms.
- maximal monotone operator,
- Banach space,
- strong convergence,
- self adaptive method
Citation: Jun Yang, Prasit Cholamjiak, Pongsakorn Sunthrayuth. Modified Tseng's splitting algorithms for the sum of two monotone operators in Banach spaces[J]. AIMS Mathematics, 2021, 6(5): 4873-4900. doi: 10.3934/math.2021286

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Abstract

In this work, we introduce two modified Tseng's splitting algorithms with a new non-monotone adaptive step size for solving monotone inclusion problem in the framework of Banach spaces. Under some mild assumptions, we establish the weak and strong convergence results of the proposed algorithms. Moreover, we also apply our results to variational inequality problem, convex minimization problem and signal recovery, and provide several numerical experiments including comparisons with other related algorithms.

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