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Iterative Solutions of Nonlinear Equations of the Strongly Accretive Type

✍ Scribed by C. E. Chidume

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
535 KB
Volume
189
Category
Article
ISSN
0025-584X

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✦ Synopsis

Let E be a real q-uniformly smooth Banach space. Suppose T is a strongly pseudocontractive map with open domain D(T) in E. Suppose further that T has a fixed point in D ( T ) . Under various continuity assumptions on T it is proved that each of the Mann iteration process or the Ishikawa iteration method converges strongly to the unique fixed point of T. Related results deal with iterative solutions of nonlinear operator equations involving strongly accretive maps. Explicit error estimates are also provided.

πŸ“œ SIMILAR VOLUMES

Iterative Solution of Nonlinear Equation
Iterative Solution of Nonlinear Equations of the Ξ¦-Strongly Accretive Type
✍ M.O. Osilike πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 159 KB

ARTICLE NO. 0203 converges strongly to the unique solution of the equation Tx s f. A related result deals with the approximation of fixed points of -hemicontractive operatorsᎏa class of operators which is much more general than the important class of strongly pseudocontractive operators.

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