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 -condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established.
"Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative." Abstr. Appl. Anal. 2013 (SI45) 1 - 11, 2013. https://doi.org/10.1155/2013/682167