Global convergence of improved Chebyshev-Secant type methods

In this paper, we present the global convergence of improved Chebyshev-Secant type methods (ICSTM) for solving nonlinear Fredholm integral equations of the second kind with non-differentiable Nemytskii operator. Existence and uniqueness theorems are established for the solution by imposing the conditions on Nemytskii operator and auxiliary points. Using recurrence relations, radii of convergence balls are obtained that ensure the convergence of iterative methods, starting from any point in the ball centered on an auxiliary point. In order to illustrate the theoretical results, we consider a nonlinear Hammerstein type integral equation that arises in the field of chemical engineering.