On coincidence point and fixed point theorems for a general class of multivalued mappings in incomplete metric spaces with an application

In this paper, weprove existence of fixed and coincidence points for a general class of multivalued mappings satisfying a new generalized contractive condition in incomplete metric spaces which generalize a number of published results in the last decades. In addition, this article not only brings a new approaches on the subject and but also involves several non-trivial examples which demonstrate the significance of the motivation. Finally, the obtained results of this paper provide a result on the convergence of successive approximations for certain operators (not necessarily linear) on a norm space (not necessarily a Banach space). In particular, we conclude that the renowned Kelisky-Rivlin theorem works on iterates of the Bernstein operators on an incomplete subspace of C[0,1].