Abstract
We are concerned with the problem of approximating a locally unique solution of a generalized equation using a multipoint method in a Banach spaces. In [9]-[11] the authors showed that the previous method is superquadratically (or cubically) convergent when the second Fréchet derivative satisfies the usual Hölder continuity condition (or center--Hölder continuity condition). Here, we weaken these conditions by using $\omega$--condition (or $\sigma$--condition) on the second derivative introduced by us [1]-[4],[22] (for nonlinear equations), with $\omega$ and $\sigma $ a non--decreasing continuous real functions. We provide also an improvement of the ratio of our algorithm under some $\omega$--center--condition (or $\sigma$--center--condition) and less computational cost.
Citation
Ioannis K. Argyros. Saïd Hilout. "Multipoint method for generalized equations under mild differentiability conditions." Funct. Approx. Comment. Math. 38 (1) 7 - 19, January 2008. https://doi.org/10.7169/facm/1229624648
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