A Strict Fixed Point Problem for δ-Asymptotically Regular Multifunctions and Well-Posedness

In 2005, Lj. Ćirić has established a fixed point theorem for asymptotically regular selfmappings of complete metric spaces. The purpose of this paper is to extend this theorem to the case of δ-asymptotically regular multifunctions on an orbitally complete metric space X which satisfy a variant of Ćirić's contractive condition. The well-posedness of the strict fixed point problem of these multifunctions is studied. We provide also a general result when the metric space X is compact. Our results are natural extensions to some recent results of Lj. B. Ćirić and some old results obtained by Sharma and Yuel and Guay and Singh. 2000 Mathematics Subject Classification. 54H25, 47H10