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Sequences of Contractions in a Generalized Metric Space

The main aim of this paper is to study the convergence of a sequence of contractions in a generalized metric space. More specifically, we investigate the following question: "If a sequence of contractions {fr } with fixed points ur (r = 1,2,...) converges to a mapping f with a fixed point u, under what conditions will the sequence u r converge to u?" A partial answer to the above question has been given in metric spaces by Bonsall [1]. This result has since been improved by Russell and Singh [6]. Further results will now be given in a generalized metric space.