scholarly journals Third-order family of methods in Banach spaces

2011 ◽  
Vol 61 (6) ◽  
pp. 1665-1675 ◽  
Author(s):  
Changbum Chun ◽  
Pantelimon Stănică ◽  
Beny Neta
Keyword(s):  
Banach Spaces ◽  
Third Order

scholarly journals Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces

1991 ◽  
Vol 4 (1) ◽  
pp. 47-69 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Index Theory ◽  
Point Theory ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Third Order ◽  
Nonnegative Solutions ◽  
Fixed Point Index Theory

In this paper, we combine the fixed point theory, fixed point index theory and cone theory to investigate the nonnegative solutions of two-point BVP for nonlinear second order integrodifferential equations in Banach spaces. As application, we get some results for the third order case. Finally, we give several examples for both infinite and finite systems of ordinary nonlinear integrodifferential equations.

scholarly journals A family of Chebyshev-Halley type methods in Banach spaces

1997 ◽  
Vol 55 (1) ◽  
pp. 113-130 ◽  
Author(s):  
J.M. Gutiérrez ◽  
M.A. Hernández
Keyword(s):  
Banach Spaces ◽  
Error Estimates ◽  
Uniqueness Of Solution ◽  
Third Order ◽  
Iterative Processes

A family of third-order iterative processes (that includes Chebyshev and Halley's methods) is studied in Banach spaces. Results on convergence and uniqueness of solution are given, as well as error estimates. This study allows us to compare the most famous third-order iterative processes.

scholarly journals Newton-Kantorovich and Smale Uniform Type Convergence Theorem for a Deformed Newton Method in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Rongfei Lin ◽  
Yueqing Zhao ◽  
Zdeněk Šmarda ◽  
Yasir Khan ◽  
Qingbiao Wu
Keyword(s):  
Banach Space ◽  
Error Estimate ◽  
Banach Spaces ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Convergence Theorem ◽  
Order Convergence ◽  
Third Order ◽  
The Third

Newton-Kantorovich and Smale uniform type of convergence theorem of a deformed Newton method having the third-order convergence is established in a Banach space for solving nonlinear equations. The error estimate is determined to demonstrate the efficiency of our approach. The obtained results are illustrated with three examples.

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