Discontinuity at fixed points with applications
R. P. Pant, Nihal Yılmaz Özgür, Nıhal Taş · Bulletin of the Belgian Mathematical Society - Simon Stevin · 2019
In this paper, we study new contractive conditions which are strong enough to generate fixed points but which do not force the map to be continuous at fixed points. In this context, we give new results on the fixed-circle problem. We investigate some applications to complex-valued metric spaces and to discontinuous activation functions in real and complex valued neural networks.