Weak and strong convergence theorems of a multistep iteration to a common fixed point of a family of nonself asymptotically nonexpansive mappings in banach spaces
In this paper we have defined a multistep iterative scheme with errors involving a family of asymptotically nonexpansive nonself mappings in Banach spaces. A retraction has been used in the construction of theiteration. We prove here weak and strong convergences of the iteration to common fixed poin...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Universidad de La Frontera
2012-10-01
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| Series: | Cubo |
| Subjects: | |
| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000300010 |
| Summary: | In this paper we have defined a multistep iterative scheme with errors involving a family of asymptotically nonexpansive nonself mappings in Banach spaces. A retraction has been used in the construction of theiteration. We prove here weak and strong convergences of the iteration to common fixed points of the family of asymptotically nonexpansive nonself mappings. We have used several concepts of Banach space geometry. Our results improve and extend some recent results.<br>En este artículo definimos un esquema de multi paso iterativo con errores que involucran una familia de aplicaciones no expansivas y no auto asintóticamente en espacios deBanach. Una retracción se ha usado en la construcción de la iteración. Probamos convergencias débiles y fuertes de las iteraciones a puntos fijos clásicos de la familia de aplicaciones no expansivas no auto asintóticamente. Hemos usado varios conceptos de geometría en espacios de Banach. Nuestro resultado mejora y extiende algunos resultados recientes. |
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| ISSN: | 0716-7776 0719-0646 |