We study the problem of proximal split feasibility of two objective convex functions in Hilbert spaces. We prove that, under suitable conditions, certain strong convergence theorems of the Halpern-type algorithm present solutions to the proximal split feasibility problem. Finally, we provide some related applications as well as numerical experiments.
"On solving proximal split feasibility problems and applications." Ann. Funct. Anal. 9 (1) 111 - 122, February 2018. https://doi.org/10.1215/20088752-2017-0028