Artículo
Rate of convergence under weak contractiveness conditions
Autor/es | Ariza Ruiz, David
Briseid, Eyvind Martol Jiménez Melado, Antonio López Acedo, Genaro |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2013 |
Fecha de depósito | 2016-10-05 |
Publicado en |
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Resumen | 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 ... 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. |
Identificador del proyecto | FQM-3543
204762/V30 MTM2007-60854 FQM-210 FQM-1504 MTM2009-13997-C02-01 FQM-127 |
Cita | 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. |
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