Volume 36 • Number 1 • 2013   • Convergence Ball Analysis of a Modified Newton's Method Under Hölder Continuous Condition in Banach Space Qingbiao Wu and Hongmin Ren Abstract. A modified Newton's method which computes derivatives every other step is used to solve a nonlinear operator equation. An estimate of the radius of its convergence ball is obtained under Hölder continuous Fréchet derivatives in Banach space. An error analysis is given which matches its convergence order. 2010 Mathematics Subject Classification: 65B05, 47817, 49D15 Full text: PDF