## Abstract and Applied Analysis

### Convergence Behavior for Newton-Steffensen’s Method under $\gamma$-Condition of Second Derivative

#### Abstract

The present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces. Under the assumption that the second derivative of the operator satisfies $\gamma$-condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 682167, 11 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393449683

Digital Object Identifier
doi:10.1155/2013/682167

Mathematical Reviews number (MathSciNet)
MR3126752

Zentralblatt MATH identifier
07095233

#### Citation

Ling, Yonghui; Xu, Xiubin; Yu, Shaohua. Convergence Behavior for Newton-Steffensen’s Method under $\gamma$ -Condition of Second Derivative. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 682167, 11 pages. doi:10.1155/2013/682167. https://projecteuclid.org/euclid.aaa/1393449683

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