Applied Mathematics, 2015, 6, 1857-1863 Published Online October 2015 in SciRes. http://www.scirp.org/journal/am http://dx.doi.org/10.4236/am.2015.611163 How to cite this paper: Saqib, M., Iqbal, M., Ahmed, S., Ali, S. and Ismaeel, T. (2015) New Modification of Fixed Point Itera- tive Method for Solving Nonlinear Equations. Applied Mathematics, 6, 1857-1863. http://dx.doi.org/10.4236/am.2015.611163 New Modification of Fixed Point Iterative Method for Solving Nonlinear Equations Muhammad Saqib 1 , Muhammad Iqbal 2 , Shahzad Ahmed 2 , Shahid Ali 2 , Tariq Ismaeel 3 1 Department of Mathematics, Govt. Degree College, Kharian, Pakistan 2 Department of Mathematics, Lahore Leads University, Lahore, Pakistan 3 Department of Mathematics, GC University, Lahore, Pakistan Email: saqib270@yahoo.com , iqbal66dn@yahoo.com , proshahzad88@gmail.com , Shahidali.2029@gmail.com , Tariqismaeel@gmail.com Received 14 August 2015; accepted 19 October 2015; published 22 October 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract In this paper, we have modified fixed point method and have established two new iterative me- thods of order two and three. We have discussed their convergence analysis and comparison with some other existing iterative methods for solving nonlinear equations. Keywords Modifications, Fixed Point Method, Nonlinear Equations 1. Introduction In recent much attention has been given to establish new higher order iteration schemes for solving nonlinear equations. Many iteration schemes have been established by using Taylor series, Adomain decomposition, Ho- motopy pertrubation technique and other decomposition techniques [1]-[6]. We shall modify the fixed point method using taylor series on the functional equation ( ) x gx = of nonlinear equation ( ) 0 f x = . Initially, we do not put any restrictions on the original function f. In fixed point method, we rewrite ( ) 0 f x = as ( ) x gx = where 1) There exist [ ] , ab such that ( ) [ ] , gx ab ∈ for all [ ] , , x ab ∈ 2) There exist [ ] , ab such that ( ) 1 gx λ ≤ < for all [ ] , , x ab ∈ The order of convergence of a sequence of approximation is defined as: Definition 1.1 [7] Let the sequence { } n x converges to α . If there is a positive integer p and real number C such that