CONVERGENCE OF THE FAMILY OF EULER-HALLEY TYPE METHODS ON RIEMANNIAN MANIFOLDS UNDER THE $\gamma$-CONDITION

Abstract

A convergence criterion of the family of Euler-Halley type methods for the vector fields on Riemannian manifolds whose covariant derivatives satisfy the $\gamma$-condition is established. The corresponding results due to [12] are extended. An application to analytic vector fields is provided.