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.