Construction and Convergence of the C-S Combined Mean Method for Multiple Polynomial Zeros

In this article, we have combined two well known third order methods one is Chebyshev and another Super- Halley to form an iterative method of for solving polynomial equations with multiple zeros. This constructed basically the mean Super-Halley, so name as C-S Combined Mean Method. We proposed some local convergence theorems Method establish computation a For establishment theorem, key role performed by function(Real valued) termed function initial conditions. Function conditions I mapping from set D into M , where (subset ) domain scheme. Here uses information only at point are given in I(w0) which belongs J interval on positive real line also contains 0 w0 starting point. used notion gauge plays very important establishing theorem. types over arbitrary normed field established method. The error estimations found our analysis. simple zero, results hold good.