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Stable Iteration Procedures for Strong Pseudocontractions and Nonlinear Equations Involving Accretive Operators without Lipschitz Assumption

✍ Scribed by Hai-Yun Zhou

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
73 KB
Volume
230
Category
Article
ISSN
0022-247X

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✦ Synopsis

Let E be a real uniformly smooth Banach space and T : E Βͺ E a strong pseudocontraction with a bounded range. We prove that the Mann and Ishikawa iteration procedures are T-stable. Some related results deal with the stability of these procedures for the iteration approximation of solutions of nonlinear equations involving accretive operators. Our results improve andror extend those corresponding results announced by Osilike.

πŸ“œ SIMILAR VOLUMES

Iterative Solution of Nonlinear Equation
Iterative Solution of Nonlinear Equations Involving Strongly Accretive Operators without the Lipschitz Assumption
✍ Haiyun Zhou πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 169 KB

Let E be a real Banach space with a uniformly convex dual space E\*. Suppose Ε½ . T : E Βͺ E is a continuous not necessarily Lipschitzian strongly accretive map Ε½ . such that I y T has bounded range, where I denotes the identity operator. It is proved that the Ishikawa iterative sequence converges str

Stable Iteration Procedures for Strong P
Stable Iteration Procedures for Strong Pseudo-contractions and Nonlinear Operator Equations of the Accretive Type
✍ M.O. Osilike πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 177 KB

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