Abstract
In this article, we investigate the notion of the pre-quasi norm on a generalized Cesaro backward difference sequence space of non-absolute type (Xi (Delta, r))psi under definite function psi. We introduce the sufficient set-up on it to form a pre-quasi Banach and a closed special space of sequences (sss), the actuality of a fixed point of a Kannan pre-quasi norm contraction mapping on (Xi (Delta, r))psi, it supports the property (R) and has the pre-quasi normal structure property. The existence of a fixed point of the Kannan pre-quasi norm nonexpansive mapping on (Xi (Delta, r))psi and the Kannan pre-quasi norm contraction mapping in the pre-quasi Banach operator ideal constructed by (Xi (Delta, r))psi and s-numbers has been determined. Finally, we support our results by some applications to the existence of solutions of summable equations and illustrative examples.