some equivalence conditions between the convergence of modified Picard, modified Mann, and modified Ishikawa iterations for some kinds of nonlinear mappings in Banach spaces are obtained.
The equivalence between Mann–Ishikawa iterations and multistep iteration
✍ Scribed by B.E Rhoades; Stefan M Soltuz
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 230 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0362-546X
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In this paper, we introduce a class of generalized quasivariational inclusions and show its equivalence with a class of fixed point problems by making use of the properties of proximal maps. Using this equivalence, we develop the Mann and Ishikawa type perturbed iterative algorithms for this class o
Let K be a nonempty compact convex subset of a uniformly convex Banach space, and T : K → 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