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.