A third order method for fixed points in Banach spaces

作者：Parhi S K; Gupta D K^*

来源：Journal of Mathematical Analysis and Applications, 2009, 359(2): 642-652.

DOI：10.1016/j.jmaa.2009.05.057

• Stirling-like method
• Holder continuity condition
• Frechet derivative
• Nonlinear operator equations

This paper deals with a third order Stirling-like method used for finding fixed points of nonlinear operator equations in Banach spaces. The semilocal convergence of the method is established by using recurrence relations under the assumption that the first Frechet derivative of the involved operator satisfies the Holder continuity condition. A theorem is given to establish the error bounds and the existence and uniqueness regions for fixed points. The R-order of the method is also shown to be equal to at least (2p + 1) for p is an element of (0, 1]. The efficacy of our approach is shown by solving three nonlinear elementary scalar functions and two nonlinear integral equations by using both Stirling-like method and Newton-like method. It is observed that our convergence analysis is more effective and give better results.

• 出版日期2009-11-15