Convergencia en procesos iterativos del punto fijo en ambientes métricos

Abstract

The theory of the fixed point, arises at the end of the XIX century and its main objective is to establish the existence and uniqueness of solutions for certain types of differential and integrable equations. In the work carried out, iterative processes are studied which are the composition of an element with itself in a repetitive way starting from a given starting point. Iterative processes are built with some extra terms that we call perturbations, showing that these processes converge to some fixed point of some operator that meets certain contractivity conditions, all this in geodesic metric spaces. The results obtained improve and extend the results reported in various papers. We also provide examples to illustrate the convergence behavior of the proposed algorithms and thus numerically compare the convergence of the proposed iterative scheme with the existing schemes.