A one-step implicit iterative process for a finite family of I-nonexpansive mappings in Kohlenbach hyperbolic spaces.

The purpose of the present paper is threefold. First, to give definition of I-nonexpansive mappings in a Kohlenbach hyperbolic space. Second, to define a new one-step implicit iterative process. Finally, to establish strong and $$\Delta $$ -convergence theorems for this iterative process in a Kohlenbach hyperbolic space. In addition, an example is provided to validate our result. Our results extend some existing results. [ABSTRACT FROM AUTHOR]