Semilocal convergence of a multipoint fourth-order super-Halley method in Banach spaces

2010 ◽  
Vol 56 (4) ◽  
pp. 497-516 ◽  
Author(s):  
Xiuhua Wang ◽  
Chuanqing Gu ◽  
Jisheng Kou
Keyword(s):  
Banach Spaces ◽  
Fourth Order ◽  
Semilocal Convergence

Deformed super-Halley’s iteration in Banach spaces and its local and semilocal convergence

2019 ◽  
Vol 30 (3-4) ◽  
pp. 413-431
Author(s):  
M. Prashanth ◽  
Abhimanyu Kumar ◽  
D. K. Gupta ◽  
S. S. Mosta
Keyword(s):  
Banach Spaces ◽  
Semilocal Convergence

Semilocal Convergence of a Seventh-Order Method in Banach Spaces Under Hölder Continuity Condition

2020 ◽  
Vol 87 (1-2) ◽  
pp. 56
Author(s):  
Neha Gupta ◽  
J. P. Jaiswal
Keyword(s):  
Banach Spaces ◽  
Error Bound ◽  
Order Of Convergence ◽  
Nonlinear Operator ◽  
Lipschitz Continuity ◽  
Semilocal Convergence ◽  
Continuity Condition ◽  
Theoretical Development ◽  
Numerical Examples ◽  
Seventh Order

The motive of this article is to analyze the semilocal convergence of a well existing iterative method in the Banach spaces to get the solution of nonlinear equations. The condition, we assume that the nonlinear operator fulfills the Hölder continuity condition which is softer than the Lipschitz continuity and works on the problems in which either second order Frèchet derivative of the nonlinear operator is challenging to calculate or does not hold the Lipschitz condition. In the convergence theorem, the existence of the solution x<sup>*</sup> and its uniqueness along with prior error bound are established. Also, the <em>R</em>-order of convergence for this method is proved to be at least 4+3q. Two numerical examples are discussed to justify the included theoretical development followed by an error bound expression.

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