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Iterative methods with mixed errors for perturbed m-accretive operator equations in arbitrary Banach spaces

✍ Scribed by Jong Soo Jung; Yeol Je Cho; Haiyun Zhou

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 589 KB
Volume: 35
Category: Article
ISSN: 0895-7177
DOI: 10.1016/s0895-7177(01)00148-0

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✦ Synopsis

X be a real Banach space, A : X + 2x a uniformly continuous m-accretive operator with nonempty closed values and bounded range R(A), and S : X + X a uniformly continuous strongly accretive operator with bounded range R(I -S). It is proved that the Ishikawa and Mann iterative processes with mixed errors converge strongly to unique solution of the equation z E Sz + XAr for given z E X and X > 0. As an immediate consequence, in case that X = 0 and S : X -+ 2x is uniformly continuous strongly accretive, some convergence theorems of Ishikawa and Mann type iterative processes with mixed errors for approximating unique solution of the equation .z E Sr are also obtained.

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