Repositorio de producción científica de la Universidad de Sevilla

Rate of convergence under weak contractiveness conditions


Advanced Search
Opened Access Rate of convergence under weak contractiveness conditions
Show item statistics
Export to
Author: Ariza Ruiz, David
Briseid, Eyvind Martol
Jiménez Melado, Antonio
López Acedo, Genaro
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2013
Published in: Fixed Point Theory, 14 (1), 11-28.
Document type: Article
Abstract: We introduce a new class of selfmaps T of metric spaces, which generalizes the weakly Zamfirescu maps (and therefore weakly contraction maps, weakly Kannan maps, weakly Chatterjea maps and quasi-contraction maps with constant h < 1 / 2). We give an explicit Cauchy rate for the Picard iteration sequences {T nx0}n∈N for this type of maps, and show that if the space is complete, then all Picard iteration sequences converge to the unique fixed point of T. Our Cauchy rate depends on the space (X, d), the map T, and the starting point x0 ∈ X only through an upper bound b ≥ d(x0, T x0) and certain moduli θ, µ for the map, but is otherwise fully uniform. As a step on the way to proving our fixed point result we also calculate a modulus of uniqueness for this type of maps.
Cite: Ariza Ruiz, D., Briseid, E.M., Jiménez Melado, A. y López Acedo, G. (2013). Rate of convergence under weak contractiveness conditions. Fixed Point Theory, 14 (1), 11-28.
Size: 235.7Kb
Format: PDF


This work is under a Creative Commons License: 
Attribution-NonCommercial-NoDerivatives 4.0 Internacional

This item appears in the following Collection(s)