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

TL;DR

This paper introduces the concept of $\sigma_c$-functions to extend Kannan's fixed point theorems, providing broader conditions for fixed point existence beyond traditional frameworks.

Contribution

It presents a new class of functions, $\sigma_c$-functions, that generalize existing fixed point theorems without relying on simulation functions, manageable functions, or R-functions.

Findings

Extended Kannan's theorems using $\sigma_c$-functions

Broader fixed point conditions established

Generalizations encompass several known results

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.