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International Journal of Analysis
Volume 2017 (2017), Article ID 7364236, 9 pages
Research Article

Influence of the Center Condition on the Two-Step Secant Method

1Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India
2Department of Mathematics, School of Arts and Sciences, Amrita Vishwa Vidyapeetham (Amrita University), Amritapuri, India

Correspondence should be addressed to Shwetabh Srivastava

Received 23 June 2017; Accepted 8 August 2017; Published 24 September 2017

Academic Editor: Shamsul Qamar

Copyright © 2017 Abhimanyu Kumar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is to present a new improved semilocal and local convergence analysis for two-step secant method to approximate a locally unique solution of a nonlinear equation in Banach spaces. This study is important because starting points play an important role in the convergence of an iterative method. We have used a combination of Lipschitz and center-Lipschitz conditions on the Fréchet derivative instead of only Lipschitz condition. A comparison is established on different types of center conditions and the influence of our approach is shown through the numerical examples. In comparison to some earlier study, it gives an improved domain of convergence along with the precise error bounds. Finally, some numerical examples including nonlinear elliptic differential equations and integral equations validate the efficacy of our approach.