A new semilocal convergence theorem for the secant method under Hölder continuous divided differences
A new Kantorovitch type convergence theorem is provided for the secant method in Banach spaces for the nonlinear operator equation \(F(x)=0\). Here \(F\) is defined on an open convex domain \(\Omega\) of a Banach space \(X\) with values in a Banach space \(Y\). The results are of interest since they apply to cases in which the known conditions failed or they were more complicated. Two examples are presented, in which the authors' conditions work, while the earlier ones fail.
scientific article; zbMATH DE number 5083662