From Kantorovich’s theory we present a semilocal convergence result for Newton’s method which is based mainly on a modification of the condition required to the second derivative of the operator involved. In particular, instead of requiring that the second derivative is bounded, we demand that it is centered. As a consequence, we obtain a modification of the starting points for Newton’s method. We illustrate this study with applications to nonlinear integral equations of mixed Hammerstein type.

From Kantorovich’s theory we present a semilocal convergence result for Newton’s method
which is based mainly on a modification of the condition required to the second derivative
of the operator involved. In particular, instead of requiring that the second derivative
is bounded, we demand that it is centered. As a consequence, we obtain a modification of
the starting points for Newton’s method. We illustrate this study with applications to
nonlinear...

Most published research on the comparison between medical treatment options merely compares the results (effectiveness and cost) obtained for each treatment group. The present work proposes the incorporation of other patient characteristics into the analysis. Most of the studies carried out in this context assume normality of both costs and effectiveness. In practice, however, the data are not always distributed according to this assumption. Alternative models have to be developed.
In...

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