The paper presents some theorems about fixed points of nonexpansive mappings certain convex subsets Banach spaces, aswell as examples applications these theorems, among others, to justify the correctness square roots approximation process in Heron’s algorithm (from 1st century AD).

In this paper, we present fixed point results for generalized contractions defined on a complete gauge space E. Also, we consider families of generalized contractions {ft : X → E}t∈[0,1] where X ⊂ E is closed and can have empty interior. We give conditions under which the existence of a fixed point for some ft0 imply the existence of a fixed point for every ft. Finally, we apply those results t...