New discontinuity results at fixed point on metric spaces

Abstract

Recently, the discontinuity problem at a fixed point has been studied by various aspects. In this paper, we investigate new solutions to the discontinuity problem using appropriate contractive conditions which are strong enough to generate fixed points (resp. common fixed points) but which do not force the map (resp. maps) to be continuous at fixed points. An application is also given to the fixed-circle problem on a metric space.