Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1991-03-31
On an Iterative Algorithm for Solving Nonlinear Operator EquationsIoannis K. Argyros (1) Cameron University, Lawton, USA
The Secant method for solving nonlinear operator equations in Banach spaces is considered. By assuming that the Fréchet derivative of a nonlinear operator is only Hölder continuous we show that the secant iteration converges to a locally unique solution. Examples are also given where our results apply and some related ones already in the literature fail.
Keywords: Banach space, Secant method, Lipschitz-Hölder continuity
Argyros Ioannis: On an Iterative Algorithm for Solving Nonlinear Operator Equations. Z. Anal. Anwend. 10 (1991), 83-92. doi: 10.4171/ZAA/433