Browder functions and theorems on fixed points and coincidences

We introduce the notion of a functional subject to a function series, the notion of a Browder function, and also the notion of a functional subject to a Browder function. We prove theorems on the search for zeros of these functionals. On the basis of this, we obtain a development, for set-valued maps, of Browder's well-known fixed-point theorem and also prove theorems on common pre-images and coincidences of maps of metric spaces which generalize some known results.