Abstract: E is A uniformly convex Banach space with the Frēchetke differentiable norm. In Space E, the convergence properties of the Mann-type iterative scheme is put under examination for the strictly pseudo-contractive countable families. The findings of this study will be popularized from a finite mapping family to an infinite mapping family, and thus weaken the space background into a real uniformly convex Babach space with the Fréchetke differentiable norms