Interpolative contractions and discontinuity at fixed point

In this paper, we investigate new solutions to the Rhoades' discontinuity problem on existence of a self-mapping which has fixed point but is not continuous at metric spaces. To do this, use number defined as n(x,y)=[d(x,y)]β[d(x,Ty)]α[d(x,Ty)]γ[(d(x,Ty)+d(x,Ty))/2]1−α−β−γ, where α , β γ ∈ ( 0,1 ) with + < 1 and some interpolative type contractive conditions. Also, geometric properties Fix(T) under contractions prove fixed-disc (resp. fixed-circle) results. Finally, present application discontinuous activation functions.