Some generalizations of Kannan's theorems via $\sigma_c$-function

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.