Jovana Džunić

TL;DR: Results are presented which describe the conjugacy classes and dynamics of the presented optimal method for complex polynomials of degree two and three and the basins of attraction of existing optimal methods and the method are compared to illustrate their performance.

TL;DR: It is demonstrated that the proposed family without memory supports the Kung–Traub hypothesis (1974) on the upper bound 2n of the order of multipoint methods based on n + 1 function evaluations.

TL;DR: It is proved that the order of convergence of the basic family without memory is eight requiring four function-evaluations, which means that this family is optimal in the sense of the Kung–Traub conjecture.

TL;DR: A wide family of three-point iterative methods for solving nonlinear equations is constructed which supports the Kung–Traub hypothesis on the upper bound 2 m of the order of multipoint methods based on m + 1 function evaluations, providing very high computational efficiency.