Watcharaporn YajaiKunrada KankamJen-Chih YaoWatcharaporn Cholamjiak2025-07-072025-07-072025Communications in Nonlinear Science and Numerical Simulation1007570410.1016/j.cnsns.2025.1089782-s2.0-105007042401https://repository.dusit.ac.th/handle/123456789/7319This paper introduces a double inertial embedded modified S-iteration algorithm for finding a common fixed point of nonexpansive mappings in a real Hilbert space. A weak convergence theorem is established under suitable conditions involving control parameters. Three algorithms are directly obtained for addressing split equilibrium problems through the equivalence of nonexpansive mappings. An illustrative example in an infinite-dimensional space is provided to substantiate the proposed main algorithm. Furthermore, we highlight the practical application of these algorithms in lung cancer screening, where they are employed to optimize three different machine learning models, thereby potentially improving patient outcomes. The efficiency of the proposed algorithms is validated through comparative analysis with existing algorithms. © 2025ClassificationDouble inertial techniqueFixed point problemLung cancerMann algorithmSplit equilibrium problemArticleScopus