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In this paper, we introduce a new class of mappings and prove the demiclosedness principle for mappings of this type in a CAT(0) space. Also, we obtain the strong and Δ-convergence theorems of new multi-step and S-iteration processes in a CAT(0) space. Our results extend and improve the corresponding recent results announced by many authors in the literature.

On the strong and Δ-convergence of new multi-step and S-iteration processes in a CAT ( 0 ) space