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Zeitschrift für Analysis und ihre Anwendungen


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Volume 10, Issue 1, 1991, pp. 83–92
DOI: 10.4171/ZAA/433

Published online: 1991-03-31

On an Iterative Algorithm for Solving Nonlinear Operator Equations

Ioannis K. Argyros[1]

(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