In this paper we study some fixed point theorems in an uniformly convex Banach space. We see these results for some contract mappings with cyclic operators of Banach type and Kannan type. We give some results on convergence of Picard operators on a spherically complete ultra metric space. Our intention is to give some existence results for approximation of the fixed points for cyclic contractions using comparison functions that can be used in algorithms.
fixed point, ultra metric space, Picard operator, cyclic contraction, comparison function.