CONVERGENCE BEHAVIOR FOR NEWTON-STEFFENSEN'S METHOD UNDER LIPSCHITZ CONDITION OF SECOND DERIVATIVE

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 Lipschitz condition, the convergence criterion and convergence ball for Newton-Steffensen's method are established. 2010Mathematics Subject Classification: 47J05, 65J15, 65H10. Key words and phrases: Newton-Steffensen's method, Majorizing function, Majorizing sequence, Lipschitz condition, Convergence criterion, Convergence radius.