Some general convergence theorems on sequences of fixed points

For each n ∈ N(naturals), let {Xn} be a sequence of nonempty subsets of a 2-metric space (X,ρ) and {Tn: Xn→ Xn} a sequence of (ψ,φ)-weakly contractive mappings with respect to a different 2-metric ρnwhich converges in some general sense to a limit mapping. We obtain a number of stability results in this paper which extend certain well known results.