Convergence Behavior for Newton-Steffensen’s Method under γ-Condition of Second Derivative

Abstract EN

The present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces.

Under the assumption that the second derivative of the operator satisfies γ-condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established.