Fixed point theorems for almost and utmost acyclic contractions

The purpose of this article is to prove fixed point theorems for new classes of acyclic mappings known as almost acyclic contractions and utmost acyclic contractions in the framework of a uniformly convex Banach space. Further, it is interesting to observe that a best proximity point theorem for cyclic contractions is elicited as an application of one of the fixed point theorems.