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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

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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