A Note on the Mann Iteration for k-Strict Pseudocontractions in Banach Spaces

We show that a variant of a previously defined function can be used to characterize 2-uniform smoothness. We then obtain greatly simplified proofs of two convergence theorems in the literature using a generalization of a lemma of and the aforementioned characterization. We also more easily obtain rates of asymptotic regularity corresponding to the studied iterations. Finally, we derive a way to relate two constants which are characteristic to 2-uniformly smooth spaces.