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Asymptotically nonexpansive mappings

✍ Scribed by W.A. Kirk; Carlos Martinez Yañez; Sang Sik Shin

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
651 KB
Volume
33
Category
Article
ISSN
0362-546X

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In this paper, we prove that if ρ is a convex, σ-finite modular function satisfying a 2 -type condition, C a convex, ρ-bounded, ρ-a.e. compact subset of L ρ , and T C → C a ρ-asymptotically nonexpansive mapping, then T has a fixed point. In particular, any asymptotically nonexpansive self-map define

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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