Abstract
We present a local convergence analysis for Euler–Halley-like methods with a parameter in order to approximate a locally unique solution of an equation in a Banach space setting. Using more flexible Lipschitz-type hypotheses than in earlier studies such as Huang and Ma (Numer Algorith 52:419–433, 2009), we obtain a larger radius of convergence as well as more precise error estimates on the distances involved. Numerical examples justify our theoretical results.
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