Convergence Of An Efficient Iterative Method For Fixed Points Under Mild Assumptions

Abstract

Many real-world applications use the concept of mathematical modelling to evaluate them through mathematical equations. Sometimes it uses the fixed point solution. However, the conditions are not so favourable to evaluate at a certain stage. We have made an attempt to use some weaker conditions on a fixed-point iterative method to solve these equations. We have provided the local convergence of such iterative method which we have proposed in [1]. We have used the weaker condition on the derivative and provide the local convergence theorem based on them. This provides the solution when the earlier condition fails. Our results are supported by some numerical examples that we provide here. This justifies the work done by us.