In this paper, we prove a strong convergence theorem by the hybrid method for a countable family of relatively nonexpansive mappings in a Banach space. We also establish a new control condition for the sequence of mappings {T n } which is weaker than the control condition in Lemma 3.1 of Aoyama et a
Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
โ Scribed by Koji Aoyama; Yasunori Kimura; Wataru Takahashi; Masashi Toyoda
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 231 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let C be a closed convex subset of a real uniformly smooth and strictly convex Banach space E. Consider the following iterative algorithm given by where f is a contraction on C and W n is a mapping generated by an infinite family of nonexpansive mappings {T i } โ i=1 . Assume that the set of common
In this paper, we introduce a new implicit iterative algorithm for finding a common element of a countable family of continuous pseudocontractions in a uniformly smooth Banach space. We obtain some strong convergence theorems under suitable conditions. Our results extend the recent results announced