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The aim of this paper is to present new sixth order iterative methods for solving nonlinear equations. The derivation of these methods is purely based on variational iteration technique. Our methods are verified by means of various test examples and numerical results show that our developed methods are more effective with respect to the previously well known methods. Finally, polynomiography via our developed method is presented which shows the dynamical behavior of our proposed methods. Received: 2017-08-23 Revised: 2017-11-18 Published: November 24, 2017 c © 2017 Academic Publications, Ltd. url: www.acadpubl.eu Correspondence author 1094 Y.C. Kwun, Z. Majeed, A. Naseem, W. Nazeer, S.M. Kang AMS Subject Classification: 47H09

New iterative methods using variational iteration technique and their dynamical behavior