Non-contractive mappings and application to a drug diffusion problem

For mappings that admit multiple fixed points, we find conditions that imply a unique fixed point. Our conclusions unify and extend numerous existing fixed point theorems. We also establish common fixed point conclusions that may not satisfy a contractive condition. Since general techniques for determining common fixed points of non-contractive mappings are not available, our results introduce new techniques for such studies. Further, we find out the geometric properties of multiple fixed points whenever there is no possibility of the persistence of a unique fixed point. An application of fixed point results has also been given to model a problem emerging while a diffusing drug is confined within an absorbing agent bounded by parallel walls with fixed concentrations.