Application of Aggregation operators in solution of nonlinear equations

Abstract

In this paper a modifications of Newton's iterative method for solving nonlinear equations based on the Aggregation operators: arithmetic, harmonic, geometric and finally the root-power mean has been considered. The convergence properties of considered methods have been analyzed. The convergence order for simple zeros is three and linear for multiple zeros. Required computational evaluations per iteration is three. By utilizing some properties of the root-power mean we suggest a most efficient method for finding the multiple zeros. Illustrative examples are given.