Semilocal convergence of Chebyshev Kurchatov type methods for non-differentiable operators

In this study, the new semilocal convergence for the family of Chebyshev Kurchatov type methods is proposed under weaker conditions. The convergence analysis demands conditions on the initial approximation, auxiliary point, and the underlying operator (Argyros et al. (2017) [10]). By utilizing the notion of auxiliary point in convergence conditions, the convergence domains are obtained where the existing results are not applicable. The theoretical results are validated using numerical examples, such as nonlinear PDE and mixed Hammerstein type integral equations originating in biology, vehicular traffic theory, and queuing theory, to determine the applicability of the proposed framework. The numerical testing shows that the new approach performed better (accurately and converge faster) than Steffensen’s method, Chebyshev type methods and two step secant method.