In this work we focus on location and approximation of a solution nonlinear integral equations Hammerstein-type when the kernel is non-separable through high order iterative process. For purpose, approximate by means separable then, perform complete study about convergence criteria for approximated obtained to our first problem. Different examples have been tested in apply theoretical results.

We discuss the solvability of a fairly general class systems perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and functionals are allowed to components system their derivatives. results applicable nonlocal second order ordinary differential subject boundary conditions, this is illustrated in an example. Our approach based class...

A plethora of sufficient convergence criteria has been provided for single-step iterative methods to solve Banach space valued operator equations. However, an interesting question remains unanswered: is it possible provide unified methods, which are weaker than earlier ones without additional hypotheses? The answer yes. In particular, we only one criterion suitable methods. Moreover, also give ...

We present an alternative approach to the vector version of Krasnosel’skiĭ compression–expansion fixed point theorem due Precup, which is based on index. It allows us obtain new general versions this and also multiplicity results. emphasize that all them are coexistence theorems for operator systems, means every component points obtained non-trivial. Finally, these applied results concerning ex...

A new parametric class of iterative schemes for solving nonlinear systems is designed. The third- or fourth-order convergence, depending on the values parameter being proven. analysis dynamical behavior this in context scalar equations presented. This study gives us important information about stability and reliability members family. numerical results obtained by applying different elements fa...