On some nonself mappings
✍ Scribed by LJ. B. Ćirić; J. S. Ume; M. S. Khan; H. K. Pathak
- Book ID
- 102490943
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 109 KB
- Volume
- 251
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
Let X be a Banach space, let K be a non–empty closed subset of X and let T : K → X be a non–self mapping. The main result of this paper is that if T satisfies the contractive–type condition (1.1) below and maps ∂K (∂K the boundary of K) into K then T has a unique fixed point in K.
📜 SIMILAR VOLUMES
In this paper, we prove some strong and weak convergence theorems using a modified iterative process for nonself asymptotically nonexpansive mappings in a uniformly convex Banach space. This will improve and generalize the corresponding results in the existing literature. Finally, we will state that
Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T 1 , T 2 : K → E be two asymptotically nonexpansive nonself-mappings with sequences where {α n } and {β n } are two real sequences in [ϵ, 1 -ϵ] for some ϵ > 0. If E