Existence of a Fixed Point for Applications on Banach Cone Spaces Using the Krasnoselskij Iteration
DOI:
https://doi.org/10.15381/pesquimat.v25i1.23141Keywords:
Krasnoselskij iteration, normal cone, metric space cone, Banach space cone, fixed pointAbstract
“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.
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Copyright (c) 2022 Jhonathan Guerrero Chirinos, Willy Barahona Mart´ınez, Edinson Montoro Alegre, Roc´ıo De La Cruz Marcacuzco
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