Convergence behavior for Newton-Steffensen's method under \(\gamma\)-condition of second derivative (Q2318969)

Summary: 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.