## A new convergence theorem for Steffensen’s method on Banach spaces and applications.(English)Zbl 0895.65024

The author proves a semilocal convergence theorem for Steffensen’s method, applied for approximating a locally unique solution of the equation $$f(x)=0$$, where $$f$$ is a twice Fréchet-differentiable continuous operator on a closed convex domain $$D$$ of a Banach space with values in a Banach space. As shown by an example, the convergence region thus obtained is larger than the ones given in other related papers.

### MSC:

 65J15 Numerical solutions to equations with nonlinear operators 47J25 Iterative procedures involving nonlinear operators
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