Fixed-point theory plays many important roles in real-world problems, such as image processing, classification problem, etc. This paper introduces and analyzes a new, accelerated common-fixed-point algorithm using the viscosity approximation method and then employs it to solve convex bilevel optimization problems. The proposed method was applied to data classification with the Diabetes, Heart Disease UCI and Iris datasets. According to the data classification experiment results, the proposed algorithm outperformed the others in the literature.

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