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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.28 n.2 Antofagasta ago. 2009

http://dx.doi.org/10.4067/S0716-09172009000200005 

Proyecciones Journal of Mathematics
Vol. 28, N° 2, pp. 155-167, August 2009.
Universidad Católica del Norte
Antofagasta - Chile



ON THE LOCAL CONVERGENCE OF A MIDPOINT METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION


Ioannis K. Argyros

Cameron University, U. S. A.


Correspondencia a:


Abstract

In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in a Banach space setting using the midpoint method, introduced by us in [5], [6]. Here, we use gamma-type condition to provide a local convergence analysis. Our results compare favorably with the relevant ones in [9], [11], [12]-[14]- In particular our radius of convergence is larger. Numerical examples are also provided.

AMS (MOS) Subject Classification codes : 65G99, 65K10, 47H17, 49M15.

Key Words : Midpoint method, Banach space, Gamma-type condition, radius of convergence, local convergence, Fréchet-derivative.



References

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IOANNIS K. ARGYROS
Cameron University
Department of Mathematical Sciences
Lawton, OK 73505
U. S. A.
e-mail : iargyros@cameron.edu


Received : October 2008. Accepted : June 2009