Kannan Nonexpansive Mappings on Nakano Sequence Space of Soft Reals with Some Applications

Abstract

We developed the operators ideal in this article by extending $s$ -soft reals and a particular space of sequences with soft real numbers. The criteria necessary for the Nakano sequence space of soft real numbers given with the definite function to be prequasi Banach and closed are investigated. This space’s ( $R$ ) and normal structural features are illustrated. Fixed points have been introduced for Kannan contraction and nonexpansive mapping. Finally, we investigate whether the Kannan contraction mapping has a fixed point in the prequasi operator ideal with which it is linked. By examining some real-world instances and their applications, it is demonstrated that there exist solutions to nonlinear difference equations.