General composite implicit iteration process for a finite family of asymptotically pseudo-contractive mappings
✍ Scribed by Balwant Singh Thakur,Rajshree Dewangan…
- Book ID
- 126376800
- Publisher
- Springer International Publishing AG
- Year
- 2014
- Tongue
- English
- Weight
- 242 KB
- Volume
- 2014
- Category
- Article
- ISSN
- 1687-1820
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📜 SIMILAR VOLUMES
Let K be a nonempty closed convex subset of a Banach space E, T : K → K a continuous pseudo-contractive mapping. Suppose that {α n } is a real sequence in [0, 1] satisfying appropriate conditions; then for arbitrary x 0 ∈ K , the Mann type implicit iteration process {x n } given by x n = α n x n-1 +
In this paper, we consider the weak and strong convergence of implicit iteration process to a common fixed point of I-asymptotically nonexpansive mappings. The main results extend to a finite family of I-asymptotically nonexpansive mappings in a Banach space.
In the present paper, we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi-nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex Banach space, requiring one member T in the family to be semicompact. Our resu