Paper Title
Convergence Study and Analysis of an Iterative Method to Solve Non- Linear Equations

In this paper, we study the semilocal convergence for a fourth-order method for solving nonlinear equations in Banach spaces. Recurrence relations are used in order to prove this convergence. We prove an existence-uniqueness theorem and Finally, we give some numerical applications to demonstrate our approach. The basins of attraction of existing methods and the presented method are given to demonstrate their performance. Keywords- Nonlinear equations in Banach spaces Recurrence relations Semilocal convergence Iterative methods Convergence domain Mathematics subject classication(2010) 65D99