A deformed Jarratt's method for solving non-linear equation in Banach space

2012 ◽  
Author(s):  
Xufeng Shang ◽  
Yubo Yuan
Keyword(s):  
Banach Space ◽  
Linear Equation ◽  
Non Linear Equation ◽  
Non Linear ◽  
Jarratt’S Method

Small solutions of a non-linear equation in Banach space for a degenerate case

1977 ◽  
Vol 79 (1-2) ◽  
pp. 35-49 ◽  
Author(s):  
M. Shearer
Keyword(s):  
Banach Space ◽  
Linear Equation ◽  
Bifurcation Theory ◽  
Degenerate Case ◽  
Schmidt Method ◽  
Degeneracy Condition ◽  
Non Linear Equation ◽  
Non Linear

SynopsisThe existence of zeroes of an operator in Banach space near a. known zero is examined, when the non-degeneracy condition of Magnus [1] is violated, and replaced by a condition which is called simple-degeneracy. Criteria are given which help determine the number and the structure of curves of zeroes of the operator, passing through the known zero.These conditions and results are interpreted in terms of bifurcation theory. By considering several different cases, it is shown that the failure of various conditions frequently employed in the Lyapunov–Schmidt method may be overcome using the idea of simple-degeneracy.

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