A Browder-Petryshyn coincidence point theorem - Berzig, Maher (Modern Mathematical Methods, 2025)
Let C be a subset of a Hilbert space, and let f and g be self-maps on C such that the range of f is a convex, closed, and bounded subset of the range of g. If f does not increase distances more than g, we demonstrate that f and g have coincidence points. This result generalizes a fixed point theorem of Browder-Petryshyn. As applications, we establish the existence of solutions to both matrix and integral equations.