On Halpern-type sequences with applications in Hadamard spaces
DOI:
https://doi.org/10.12775/TMNA.2024.038Keywords
Fixed point, Hadamard space, Halpern sequence, resolvent operator, strong convergenceAbstract
We introduce the concept of quasi-Halpern sequence which generalizes the concept of Halpern sequences introduced by Jaipranop and Saejung \cite{JS-2020} from Hilbert spaces to Hadamard spaces. Our notion also allows some error computation in the sequence. Furthermore, we establish a necessary and sufficient condition for the strong convergence of a quasi-Halpern sequence. Additionally, we have derived two strong convergence theorems for approximating fixed points of nonexpansive sequences or strongly quasi-nonexpansive sequences. Moreover, we apply our results to the problem of finding a zero of a certain monotone operator and a minimizer of a convex function in a Hadamard space. Our result generalizes and improves the recent results of Kohsaka and Kimura \cite{KK-2016} and of Okeke \cite{O-2023}.References
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