A family of newton type iterative processes

Abstract

In this paper, we define an index of the convexity measure by means of the logarithmic operator. As an application, we study the influence of the convexity on Newton method for solving nonlinear equations. Then we define a family of Newton type iterative processes to solve a complex or scalar nonlinear equation, we can always apply an iterative process of this family faster than Newton method.

Keywords:

• Nonlinear equations
• Iterative processes
• Optimization
• Convexity

Classification A.M.S. 1985:

• 65H05
• 26A51

C.R Categories:

• 5.1
• 5.1.5