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In this paper we extend to $UCW$-hyperbolic spaces the quantitativeasymptotic regularity results for the alternating Halpern-Mann iterationobtained by Dinis and the second author for CAT(0) spaces. These results arenew even for uniformly convex normed spaces. Furthermore, for a particularchoice of the parameter sequences, we compute linear rates of asymptoticregularity in $W$-hyperbolic spaces and quadratic rates of $T$- and$U$-asymptotic regularity in CAT(0) spaces.

Rates of asymptotic regularity for the alternating Halpern-Mann iteration