Existence of a Fixed Point for Applications on Banach Cone Spaces Using the Krasnoselskij Iteration - Guerrero Chirinos, Jhonathan (2022)
“Given a closed and convex subset C of a cone Banach space E with norm ∥x∥P = d (x, 0) and a map T : C → C that satisfies the condition for all x, y ∈ C 0 ≤ s + |a| − 2b < 2(a + b) ad (T x, T y) + b (d (x, T x) + d (y, T y)) ≤ sd (x, y) The general objective of this article is to demonstrate the existence of at least one fixed point for the map T , for which we will use a particular case of the Krasnoselskij iteration.