Linear rates of asymptotic regularity for Halpern-type iterations

In this note we apply a lemma due to Sabach and Shtern to compute linear rates of asymptotic regularity for Halpern-type nonlinear iterations studied in optimization and nonlinear analysis

Hybrid algorithm with perturbations for total asymptotically non-expansive mappings in CAT(0) space

In this paper, we establish strong and Δ-convergence theorems of the modified hybrid-CR three steps iteration with perturbations for total asymptotically non-expansive mapping in CAT(0) spaces. Our results improve and extend the corresponding results from the current literature. We also provide three examples to illustrate the convergence behaviour of the proposed algorithm and numerically compare the convergence of the proposed iteration scheme with the existing schemes