Convergence of the family of the deformed Euler-Halley iterations under the Holder condition of the second derivative

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:194

Article

Ye, Xintao ; Li, Chong

关键词: nonlinear operator equation;    the family of the deformed Euler-Halley iterations;    the Holder condition;   

DOI  :  10.1016/j.cam.2005.07.019

来源: Elsevier

【 摘 要 】

The convergence problem of the family of the deformed Euler-Halley iterations with parameters for solving nonlinear operator equations in Banach spaces is studied. Under the assumption that the second derivative of the operator satisfies the Holder condition, a convergence criterion of the order 2+p of the iteration family is established. An application to a nonlinear Hammerstein integral equation of the second kind is provided. (c) 2005 Elsevier B.V. All rights reserved.

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