Dipartimento di Matematica, Universitá della Calabria, 87036 Rende (Cosenza), Italy ; Dipartimento di Matematica Applicata ``U.Dini', Via Bonanno Pisano 25/B, 56126 Pisa, Italy
Abstract:
The use of K-normed spaces gives us the possibility to prove that a fixed point theorem due to B. Luo is equivalent to the Banach Contraction Principle. This confirms the conspiracy among fixed point theorems. Moreover the theorem of Lou is improved and extended to different contexts. A counterexample about the fixed points of the sum of a contraction and an integral operator is given. The usefulness of K-norm is tested on a Volterra integral equation as well.