A new extension of Kannan contractions and related fixed point results

The aim of this study is to introduce a new generalized family of contraction mapping called F-Kannan contractions. We have stated an error in an earlier attempt made in this direction and have justified this by illustrating it with an example. We claim that our approach is completely analogous to the concept of F-Contractions. A fixed point result have been proved for our extended class of contraction mapping and also for a weaker class of F-Kannan mapping on a non complete metric space. We have also proved that Subrahmanyam's characterization of completeness of a metric space involving Kannan mapping remains valid in case of our extended class of contractions.