An algorithm for variational inclusion problems including quasi-nonexpansive mappings with applications in osteoporosis prediction

Raweerote Suparatulatorn; Wongthawat Liawrungrueang; Thanasak Mouktonglang; Watcharaporn Cholamjiak; Raweerote Suparatulatorn; Wongthawat Liawrungrueang; Thanasak Mouktonglang; Watcharaporn Cholamjiak

doi:10.3934/math.2025118

AIMS Mathematics

2025, Volume 10, Issue 2: 2541-2561. doi: 10.3934/math.2025118

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Research article

An algorithm for variational inclusion problems including quasi-nonexpansive mappings with applications in osteoporosis prediction

1.
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2.
Office of Research Administration, Chiang Mai University, Chiang Mai 50200, Thailand
3.
Department of Orthopaedics, School of Medicine, University of Phayao, Phayao 56000, Thailand
4.
School of Science, University of Phayao, Phayao 56000, Thailand

Received: 20 November 2024 Revised: 10 January 2025 Accepted: 15 January 2025 Published: 12 February 2025
MSC : 47J25, 49M37, 90C90

This paper has proposed a novel algorithm for solving fixed point problems for quasi-nonexpansive mappings and variational inclusion problems within a real Hilbert space. The proposed method exhibits weak convergence under reasonable assumptions. Furthermore, we applied this algorithm for data classification to osteoporosis risk prediction, utilizing an extreme learning machine. From the experimental results, our proposed algorithm consistently outperforms existing algorithms across multiple evaluation metrics. Specifically, it achieved higher accuracy, precision, and F1-score across most of the training boxes compared to other methods. The area under the curve (AUC) values from the receiver operating characteristic (ROC) curves further validated the effectiveness of our approach, indicating superior generalization and classification performance. These results highlight the efficiency and robustness of our proposed algorithm, demonstrating its potential for enhancing osteoporosis risk-prediction models through improved convergence and classification capabilities.
- variational inclusion problem,
- fixed point problem,
- osteoporosis,
- process innovation
Citation: Raweerote Suparatulatorn, Wongthawat Liawrungrueang, Thanasak Mouktonglang, Watcharaporn Cholamjiak. An algorithm for variational inclusion problems including quasi-nonexpansive mappings with applications in osteoporosis prediction[J]. AIMS Mathematics, 2025, 10(2): 2541-2561. doi: 10.3934/math.2025118

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Abstract

This paper has proposed a novel algorithm for solving fixed point problems for quasi-nonexpansive mappings and variational inclusion problems within a real Hilbert space. The proposed method exhibits weak convergence under reasonable assumptions. Furthermore, we applied this algorithm for data classification to osteoporosis risk prediction, utilizing an extreme learning machine. From the experimental results, our proposed algorithm consistently outperforms existing algorithms across multiple evaluation metrics. Specifically, it achieved higher accuracy, precision, and F1-score across most of the training boxes compared to other methods. The area under the curve (AUC) values from the receiver operating characteristic (ROC) curves further validated the effectiveness of our approach, indicating superior generalization and classification performance. These results highlight the efficiency and robustness of our proposed algorithm, demonstrating its potential for enhancing osteoporosis risk-prediction models through improved convergence and classification capabilities.

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