Rate of convergence under weak contractiveness conditions
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 se...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/47033 |
| Acceso en línea: | http://hdl.handle.net/11441/47033 |
| Access Level: | acceso abierto |
| Palabra clave: | Cauchy rate Wweakly Zamfirescu maps Weakly contractive maps Quasi-contraction maps Modulus of uniqueness Rate of convergence Fixed points |
| Sumario: | 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. |
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