On discontinuity problem with an application to threshold activation function

Abstract

In this paper, some discontinuity results are obtained using the number $%
M_{C}(x,y)$ at the common fixed point. Our results provide a solution to an
open problem "What are the contractive conditions which are strong enough to generate a fixed point but which do not force the map to be continuous at fixed point?" given by Rhoades \cite{Rhoades-2}. To do this, we
investigate a new theorem gives us a discontinuity result at the common
fixed point on a complete metric space. Also an application to
threshold activation function is given.