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This paper deals with the validation of convergence results for the newly proposed C- non-expansive mappings in the CAT(0) space setting.Before analyzing the convergence behavior, we emphasize key results related to C- non-expansive mappings.The convergence results are obtained using the JF -iteration method.We then illustrate these results with non-trivial examples and compare them to other notable iterations.These comparisons are presented in both tabular and graphical forms.Finally, we discuss a variational inequality problem within the context of these mappings using the same iteration scheme.
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