Abstract
We study a nonlinear semigroup associated with a nonexpansive mapping on an Hadamard space and establish its weak convergence to a fixed point. A discrete-time counterpart of such a semigroup, the proximal point algorithm, turns out to have the same asymptotic behavior. This complements several results in the literature—both classical and more recent ones. As an application, we obtain a new approach to heat flows in singular spaces for discrete as well as continuous times.
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To Professor Andrzej Granas with appreciation and respect
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Bačák, M., Reich, S. The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces. J. Fixed Point Theory Appl. 16, 189–202 (2014). https://doi.org/10.1007/s11784-014-0202-3
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DOI: https://doi.org/10.1007/s11784-014-0202-3