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...

Abstract The aim of this paper is to introduce a new class mixed contractions which allow revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih Imdad. We also provide an example corresponding mappings show how the fixed point result relates above-mentioned [6]. Further, we present application solvability two-point boundary value problem for second order differential equ...