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DOI: 10.23952/jnfa.2023.26
Received May 22, 2023; Accepted July 18, 2023; Published August 10, 2023
Abstract. This paper presents our investigation into the split feasibility problem with multiple output sets (SFPMOS), under the assumption that the corresponding convex subsets are level subsets of convex functionals. To approximate the solutions of this problem, we propose a method that combines relaxed projection with a recently proposed technique. Our approach involves establishing a weak convergence theorem for the fixed stepsize, followed by constructing a variable stepsize that is independent of the norm of the linear operator involved. We also modify these methods to ensure strong convergence. As an application, we develop a new relaxed projection algorithm for solving the split feasibility problem.
How to Cite this Article:
L. Xue, H. Cui, On the relaxed projection method for the SFPMOS, J. Nonlinear Funct. Anal. 2023 (2023) 26.