Some new results on stability of fixed points

Using some new notions of convergence, Barbet and Nachi [Barbet L, Nachi K. Sequences of contractions and convergence of fixed points. Monografias del Seminario Matemático García de Galdeano 2006;33:51–58.] obtained several interesting results on the stability of fixed points in a metric space. These results are extended to 2-metric spaces which differ topologically from metric spaces in many ways.