Semilocal convergence of a computationally efficient iterative method in Banach spaces under weak condition

2017 ◽  
Vol 28 (1) ◽  
pp. 141-154 ◽  
Author(s):  
J. P. Jaiswal
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Semilocal Convergence ◽  
Weak Condition ◽  
Computationally Efficient

scholarly journals A NOTE ON THE SEMILOCAL CONVERGENCE OF CHEBYSHEV’S METHOD

2012 ◽  
Vol 88 (1) ◽  
pp. 98-105 ◽  
Author(s):  
MANUEL A. DILONÉ ◽  
MARTÍN GARCÍA-OLIVO ◽  
JOSÉ M. GUTIÉRREZ
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Nonlinear Equations ◽  
Semilocal Convergence ◽  
Iterative Processes ◽  
Chebyshev’S Method

AbstractIn this paper we develop a Kantorovich-like theory for Chebyshev’s method, a well-known iterative method for solving nonlinear equations in Banach spaces. We improve the results obtained previously by considering Chebyshev’s method as an element of a family of iterative processes.

scholarly journals Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Abhimanyu Kumar ◽  
Dharmendra K. Gupta ◽  
Eulalia Martínez ◽  
Sukhjit Singh
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Local Convergence ◽  
Recurrence Relations ◽  
Semilocal Convergence ◽  
Convergence Domain ◽  
Differentiability Condition ◽  
Type Integral ◽  
Weaker Conditions ◽  
Theoretical Results

The semilocal and local convergence analyses of a two-step iterative method for nonlinear nondifferentiable operators are described in Banach spaces. The recurrence relations are derived under weaker conditions on the operator. For semilocal convergence, the domain of the parameters is obtained to ensure guaranteed convergence under suitable initial approximations. The applicability of local convergence is extended as the differentiability condition on the involved operator is avoided. The region of accessibility and a way to enlarge the convergence domain are provided. Theorems are given for the existence-uniqueness balls enclosing the unique solution. Finally, some numerical examples including nonlinear Hammerstein type integral equations are worked out to validate the theoretical results.

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
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