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\(\Delta\)-convergences of weighted averaged projections in \(\mathrm{CAT}(\kappa)\) spaces. (English) Zbl 07356497

Summary: We first introduce the weighted averaged projection sequence in \(\mathrm{CAT}(\kappa)\) spaces and then we establish some inequalities for the weighted averaged projection sequence. Using the inequalities, we prove the asymptotic regularity and the \(\Delta\)-convergence of the weighted averaged projection sequence. Furthermore, we prove the strong convergence of the sequence under certain regularity or compactness conditions on \(\mathrm{CAT}(\kappa)\) spaces.

MSC:

47J25 Iterative procedures involving nonlinear operators
47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
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