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Ishikawa and Mann iteration methods for nonlinear strongly accretive mappings

Published online by Cambridge University Press:  17 April 2009

M.O. Osilike
M.O. Osilike
Affiliation:
Department of Mathematics, University of Nigeria, Nsukka Nigeria
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Abstract

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Let X be a real Banach space with a uniformly convex dual, X*, and let C be a nonempty closed convex and bounded subset of X. Let T: C → C be a strongly accretive and a continuous mapping. For any f ∈ C, let S: C → C be defined by Sx = f + x – Tx for each x ∈ C. Then, the iteration process xo ∈ C,

under suitable conditions on the real sequence converges strongly to a solution of the equation Tx = f in C. Furthermore, if T is strongly accretive and Lipschitz with Lipschitz constant L ≥ 1 then the iteration process x0 ∈ C,

under suitable conditions on the real sequences and converges strongly to a solution of the equation Tx = f in C. Explicit error estimates are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 3 , December 1992 , pp. 413 - 424
Copyright
Copyright © Australian Mathematical Society 1992

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