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Ishikawa and Mann Iteration Methods with Errors for Nonlinear Equations of the Accretive Type

✍ Scribed by M.O. Osilike

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
212 KB
Volume
213
Category
Article
ISSN
0022-247X

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✦ Synopsis

114᎐125 converge strongly to the solution of the equation Tx s f. Furthermore, if E is a uniformly smooth Banach space and T : E Βͺ E is demicontinuous and strongly accretive, it is also proved that both the Ishikawa and the Mann iteration methods with errors converge strongly to the solution of the equation Tx s f. Related results deal with the iterative approximation of fixed points of strongly pseudocontractive operators, and the solution of the equation x q Tx s f, f g E when T : E Βͺ E is m-accretive.

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## Abstract The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let __X__ be a real Banach space and __T__ : __D__ βŠ‚ __X__ β†’ 2

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It is proved that certain Mann and Ishikawa iteration procedures are stable with respect to strongly pseudo-contracti¨e mappings in real Banach spaces which are q-uniformly smooth, 1q -ϱ. A related result deals with stable iteration procedures for solutions of nonlinear equations of the accreti¨e ty