On stable fixed points under several kinds of strong perturbations

Abstract

This gives new results on stable fixed points related to several kinds of strong perturbations in references. It is shown that a strong stable set of fixed points has a robust stable property. For a robust stable fixed point set of a correspondence, in its neighborhood, there is a strong stable set for any small perturbation of the correspondence. There exists a robust stable set for a correspondence, if there is at least one fixed point for the correspondence. These generalize the corresponding results in recent references and give an application in the existence of strong stable economy equilibria.

Multidimensional fixed points in generalized distance spaces

“…Most of the problems of applied mathematics are reduced to finding fixed points of certain mappings. For solving various problems of integral calculus, researchers have tried to generalize contractive conditions, mappings, and metric spaces, see [6][7][8][9][10][11]17]. Clearly, G ∈ C(I).…”