Results on Discontinuity at Fixed Point for a New Class of F-Contractive Mappings

The search for contractive definitions which do not compel the mapping to be continuous at fixed points remained an open problem for a long time. Several solutions to this open prob-lem have been obtained in last two decades. The current paper, we aim to provide another new solution direction for the discontinuity study at fixed points using F -contractive mappings in a complete metric space. Several consequences of those new results are also provided. This manuscript consists of three main parts. In the first part, the notion of F -contractive mappings has been described. In the second part, discontinuity at the fixed point assuming continu-ity of the composition has been investigated, whereas in the third part, discontinuity at a fixed point without assuming continuity of the composition has been illustrated.