  In this paper, we explain a new Iterative Method-Fixed Point and develop its
convergence theory for finding approximate solutions of nonlinear equations in
the setting of Banach spaces. First, we discuss the convergence analysis of our
method by separating the equation into functions from which it is derived and
the remaining part of the equation, according to the Generalized Theorem[1] for
solving polynomial and transcendental equations. Solving an equation, either
polynomial or transcendental, is solved only by categorizing the roots and not
by some procedure of searching in individual intervals and this way was
followed in the past by all existing methods. But the methods developed in the
past are limited to isolated intervals without general acceptance. Finally, the
method is strengthened by Newton's method to speed up the finding of the roots.
At the end of the analysis, we give several examples of the application of the
method.
