Some convergence results for a sequence of Gornicki type contraction mappings

Abstract

The stability of fixed points for a sequence of mappings {T_n} satisfying the conditions introduced by Gornicki is studied in a metric space (X,d). In particular, these mappings are only defined on a subset X_n of the metric space X. In this paper we study the convergence of {T_n} and the convergence of their fixed points {x_n}. We also illustrate our results by applying them to an initial value problem for an ordinary differential equation.