Abstract
The significance of our work is to solve some second-order nonlinear boundary value problems. To do this, we take into account the equivalence of the problems considered with certain integral equations, we will obtain a fixed-point-type result for these integral equations. This result provides us the existence and uniqueness of solutions for the second-order nonlinear boundary value problems considered. As a novelty, we will use for this fixed-point-type result a family of third order iterative processes to approximate the solution, instead of the usually considered method of Successive Approximations of linear convergence.
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