Two step Steffensen-type methods with or without memory for nondifferentiable equations

A wide range of applications emerging from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean multidimensional, Hilbert or Banach to mention a few, a plethora of which are nondifferentiable. Different methodologies are developed worldwide to handle the solutions of such equations. Such methodologies can also be applied to solve the differentiable equations. In the current study, two step Steffensen-Type methods with and without memory free from derivatives are considered for the nondifferentiable equations and the local as well as semilocal convergence analysis is proved under more generalized conditions. Numerical applications are provided which demonstrate the theoretical results. Better results in terms of radii of convergence balls and number of iterations are obtained using the proposed approach as compared to the existing ones.