Let K be a nonempty compact convex subset of a uniformly convex Banach space, and T : K β P(K ) a multivalued nonexpansive mapping. We prove that the sequences of Mann and Ishikawa iterates converge to a fixed point of T . This generalizes former results proved by Sastry and Babu [K.P.R. Sastry, G.V
β¦ LIBER β¦
Convergence of iterative algorithms for multivalued mappings in Banach spaces
β Scribed by Yisheng Song; Hongjun Wang
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 484 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0362-546X
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Let E be a uniformly convex Banach space having a uniformly GΓ’teaux differentiable norm, D a nonempty closed convex subset of E, and T : D β K (E) a nonself multimap such that F (T ) = β and P T is nonexpansive, where F (T ) is the fixed point set of T , K (E) is the family of nonempty compact subse