On the local convergence of a midpoint method in banach spaces under a gamma-type condition


  • Ioannis K. Argyros Cameron University.




Midpoint method, Banach space, Gamma—type condition, Radius of convergence, Local convergence, Fréchet—derivative.


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.

Author Biography

Ioannis K. Argyros, Cameron University.

Department of Mathematical Sciences.


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How to Cite

I. K. Argyros, “On the local convergence of a midpoint method in banach spaces under a gamma-type condition”, Proyecciones (Antofagasta, On line), vol. 28, no. 2, pp. 155-167, 1.




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