Abstract
In this paper, we consider the multiple-set split common fixed point problem in Hilbert spaces. We first study a couple of critical properties of strictly pseudocontractive mappings and particularly the property under mix activity. By utilizing these properties, we propose new iterative strategies for settling this problem as well as several connected issues. Under delicate conditions, we state weak convergence of the proposed strategies that expands the current works from the case of two subsets to the instance of multiple subsets. As an application, we give an exhibit of the theoretical results to the multiple-set split equality problem and the elastic net regularization.
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