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

• Argyros, Ioannis K. ^[1]
  1. [1] Cameron University

     Cameron University

     Estados Unidos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 28, Nº. 2, 2009, págs. 155-167
• Idioma: inglés
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• Resumen

  • 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.