Well-Posedness of Fixed Point Problem for a Multifunction Satisfying an Implicit Relation

Mohamed Akkouchi, Valeriu Popa

The notion of well-posedness of a fixed point problem for a single valued mapping has generated much interest to a several mathematicians, for examples, F.S. De Blassi and J. Myjak (1989), S. Reich and A. J. Zaslavski (2001), B.K. Lahiri and P. Das (2005) and V. Popa (2006 and 2008). In this paper we extend the notion of well-posedness known for single valued mappings to the case of multifunctions. We establish the well-posedness of fixed point problem for a multifunction satisfying an implicit relation in orbitally complete metric spaces.