On Strong convergence of Halpern's method using averaged type mappings
Filomena Cianciaruso, Giuseppe Marino, Angela Rugiano, Bruno, Scardamaglia
TL;DR
This paper investigates the strong convergence of Halpern's iterative method for fixed points of nonexpansive and nonspreading mappings, utilizing averaged type mappings for regularization.
Contribution
It extends Halpern's method analysis by incorporating averaged type mappings to ensure strong convergence in fixed point approximation.
Findings
Established strong convergence results for Halpern's method
Utilized averaged type mappings for regularization
Extended previous convergence analyses
Abstract
In this paper, inspired by Iemoto and Takahashi [S. Iemoto, W. Takahashi, Nonlinear Analysis 71, (2009), 2082-2089], we study the Halpern's method to approximate strongly fixed points of a nonexpansive mapping and of a nonspreading mapping. A crucial tool in our results is the regularization with the averaged type mappings [C. Byrne, Inverse Probl. 20, (2004), 103-120].
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Taxonomy
TopicsOptimization and Variational Analysis · Numerical methods in inverse problems · Advanced Optimization Algorithms Research