Title: Some generalizations of Kannan's theorems via $σ_c$-function,
Abstract: In this article we go on to discuss about various proper extensions of
Kannan's two different fixed point theorems, introducing the new concept of
$\sigma_c$-function; which is independent of the three notions of simulation
function, manageable functions and R-functions. These results are the analogous
to some well known theorems, and extends several known results in this
literature.