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

Abstract

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 $\gamma$-condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established.