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Iterative Process with Errors of Nonlinear Equations Involvingm-Accretive Operators

โœ Scribed by Xie Ping Ding

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
176 KB
Volume
209
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

Let X be a uniformly smooth and uniformly convex Banach space and T : D T ลฝ .

ลฝ . ; X ยช X be an m-accretive operator with the domain D T and the range R T . For any given f g X, we prove that the Mann and Ishikawa type iterative sequences with errors converge strongly to the unique solution of the equation x q Tx s f where T may not be Lipschitz. Some related results deal with the convergence of Mann and Ishikawa type iterative sequences with errors for approximating a solution of a continuous dissipative operator equation. แฎŠ 1997 Academic Press

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Iterative Solution of Nonlinear Equation
Iterative Solution of Nonlinear Equations Involving Strongly Accretive Operators without the Lipschitz Assumption
โœ Haiyun Zhou ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 169 KB

Let E be a real Banach space with a uniformly convex dual space E\*. Suppose ลฝ . T : E ยช E is a continuous not necessarily Lipschitzian strongly accretive map ลฝ . such that I y T has bounded range, where I denotes the identity operator. It is proved that the Ishikawa iterative sequence converges str

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โœ M.O. Osilike ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 212 KB

114แŽ125 converge strongly to the solution of the equation Tx s f. Furthermore, if E is a uniformly smooth Banach space and T : E ยช 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