scholarly journals Brakhage's Implicit Iteration Method and the Information Complexity of Equations with Operators Having Closed Range

1999 ◽  
Vol 15 (3) ◽  
pp. 385-401 ◽  
Author(s):  
Sergei V Pereverzev ◽  
Eberhard Schock
Keyword(s):  
Iteration Method ◽  
Information Complexity ◽  
Closed Range ◽  
Implicit Iteration

scholarly journals Approximation of common fixed points of a finite family of Ø - demicontractive mappings by an implicit iteration method.

2015 ◽  
Vol 12 (1) ◽  
pp. 31-38
Author(s):  
DI Igbokwe ◽  
UE Udofia
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Iteration Method ◽  
Iteration Process ◽  
Common Fixed Points ◽  
Finite Family ◽  
Implicit Iteration Process ◽  
Demicontractive Mappings ◽  
Implicit Iteration

We prove that the Implicit Iteration process of Xu and Ori (2001) converges strongly to the commonfixed pointsof a finite family of Ø - demicontractive mappings in real Hilbertand Banachspaces. Our results extend the results of Osilike (2004a) from strictl pseudocontractive maps to the much more general Ø - demicontractive maps;complement and generalize several others in the literature.KEY WORDS AND PHRASES: Ø - Demicontractive Maps, Implicit Iteration Process, Fixed Points,Strong Convergence.

scholarly journals Numerical differentiation for two-dimensional scattered data on arbitrary domain base on Hermite extension with an implicit iteration process

2022 ◽  
Vol 7 (4) ◽  
pp. 5991-6015
Author(s):  
Benxue Gong ◽  
◽  
Zhenyu Zhao ◽  
Tiao Bian ◽  
Yingmei Wang ◽  
...  
Keyword(s):  
Iteration Method ◽  
Input Data ◽  
Solution Process ◽  
Iteration Process ◽  
Numerical Differentiation ◽  
Scattered Data ◽  
Two Dimensional ◽  
Arbitrary Domain ◽  
Approximation Process ◽  
Implicit Iteration

<abstract><p>In this paper, we develop a method for numerical differentiation of two-dimensional scattered input data on arbitrary domain. A Hermite extension approach is used to realize the approximation and a modified implicit iteration method is proposed to stabilize the approximation process. For functions with various smooth conditions, the numerical solution process of the method is uniform. The error estimates are obtained and numerical results show that the new method is effective. The advantage of the method is that it can solve the problem in any domain.</p></abstract>

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