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Generalized Halpern iteration with new control conditions and its application

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Abstract

In this paper, we investigate the generalized Halpern iteration for computing fixed points of nonexpansive mappings in Hilbert space setting, and prove the strong convergence under new control conditions on parameters. The convergence results generalize the existing ones in the literature. We also present a convergence rate analysis for the generalized Halpern iteration with a particular choice of parameters. Finally, we give an application to the split feasibility problem and two numerical examples for illustrating the performance of the algorithm.

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Funding

This work is supported by the National Natural Science Foundation of China (Nos. 11971216, 62072222).

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  1. Department of Mathematics, Luoyang Normal University, Luoyang, 471022, China

    Hai Yu & Fenghui Wang

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  1. Hai Yu
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  2. Fenghui Wang
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Contributions

HY contributed to the conception of the study, wrote the main manuscript text, and performed the experiment. FW contributed significantly to analysis and manuscript preparation and helped perform the analysis with constructive discussions. All authors reviewed the manuscript.

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Correspondence to Hai Yu.

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Yu, H., Wang, F. Generalized Halpern iteration with new control conditions and its application. J. Fixed Point Theory Appl. 25, 45 (2023). https://doi.org/10.1007/s11784-023-01050-2

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