Development of a Higher-Order Iterative Method with Variable Parameters for the Roots of Starlike Functions

Abstract

In this present paper, a new iterative scheme is obtained, designed to compute the roots of starlike functions and to address the constrains faced by traditional iterative algorithms when dealing with this specific class of functions. This is achieved by combining the development formula with coefficients of the variable m and α, which demonstrating that both the order of convergence and computational efficiency improve as these coefficients increase. The numerical examples confirm the proposed scheme's ability to solve the drawbacks of classical methods, achieving high numerical efficiency and a convergence rate that is faster compared to known traditional methods.