Iterative manner involving sunny nonexpansive retractions for nonlinear operators from the perspective of convex programming as applicable to differential problems, image restoration and signal recovery

Damrongsak Yambangwai; Chonjaroen Chairatsiripong; Tanakit Thianwan; Damrongsak Yambangwai; Chonjaroen Chairatsiripong; Tanakit Thianwan

doi:10.3934/math.2023361

AIMS Mathematics

2023, Volume 8, Issue 3: 7163-7195. doi: 10.3934/math.2023361

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Research article

Iterative manner involving sunny nonexpansive retractions for nonlinear operators from the perspective of convex programming as applicable to differential problems, image restoration and signal recovery

Department of Mathematics, School of Science, University of Phayao, Phayao, 56000, Thailand

Received: 28 August 2022 Revised: 09 December 2022 Accepted: 04 January 2023 Published: 11 January 2023
MSC : 46T99, 47H09, 47H10, 47J25, 49M37, 54H25

In this paper, using sunny nonexpansive retractions which are different from the metric projection in Banach spaces, we develop the $ CR $-iteration algorithm in view of two quasi-nonexpansive nonself mappings and also give the convergence analysis for the proposed method in the setting of uniformly convex Banach spaces. Furthermore, our results can be applied for the purpose of finding common zeros of accretive operators, convexly constrained least square problems and convex minimization problems. Regarding application, some numerical experiments involving real-world problems are provided, with focus on differential problems, image restoration problems and signal recovery problems.
- convexly constrained least square problem,
- convex minimization problem,
- signal recovery problem,
- image restoration problem,
- sunny nonexpansive retract
Citation: Damrongsak Yambangwai, Chonjaroen Chairatsiripong, Tanakit Thianwan. Iterative manner involving sunny nonexpansive retractions for nonlinear operators from the perspective of convex programming as applicable to differential problems, image restoration and signal recovery[J]. AIMS Mathematics, 2023, 8(3): 7163-7195. doi: 10.3934/math.2023361

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Abstract

In this paper, using sunny nonexpansive retractions which are different from the metric projection in Banach spaces, we develop the $ CR $-iteration algorithm in view of two quasi-nonexpansive nonself mappings and also give the convergence analysis for the proposed method in the setting of uniformly convex Banach spaces. Furthermore, our results can be applied for the purpose of finding common zeros of accretive operators, convexly constrained least square problems and convex minimization problems. Regarding application, some numerical experiments involving real-world problems are provided, with focus on differential problems, image restoration problems and signal recovery problems.

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