Results on condensed Kannan-type 2-cyclic map in b-metric spaces

Abstract

Some authors recently proposed a condensed Kannan-type map that can solve nonlinear problems with unique and non-unique solutions. However, these findings may not address all situations involving inexact spaces. This study presents a strategy for proving fixed points of Kannan-type 2-cyclic contractions by condensation in inexact spaces, commonly referred to as b-metric spaces. We further extend the findings to study fixed points of trivially cyclic mappings. With the aid of examples comprising cyclic and trivially cyclic mappings, we validate all hypotheses of this study. The results show that the condensed cyclic Kannan-type map is more elaborate than the previous Kannan-type cyclic maps in the literature, solves problems with the inexact structures, and ensures unique and non-unique fixed points.