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Ishikawa and Mann Iterative Processes with Errors for Nonlinear Strongly Accretive Operator Equations

✍ Scribed by Yuguang Xu


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
140 KB
Volume
224
Category
Article
ISSN
0022-247X

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Ishikawa and Mann Iteration Methods with
✍ M.O. Osilike πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 212 KB

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

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Let X be a uniformly smooth and uniformly convex Banach space and T : D T Ε½ . Ε½ . ; X Βͺ 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

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✍ Ljubomir B. Δ†iriΔ‡; Jeong Sheok Ume πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 151 KB πŸ‘ 1 views

## 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