Some Fixed-Function Results on S-Metric Spaces with an Application to the Treatment Plan for Tumour Patients

In this study, fixed-function results are established in the framework of S-metric spaces under both Banach-type and Reich-type contractive conditions.These results extend classical fixed-point theory to a functional settingand ensure the existence and uniqueness of fixed functions in generalizedmetric spaces. Moreover, the Banach-type fixed function theorem is appliedto obtain the best approximation of treatment plans for tumour patientsundergoing intensity modulated radiation therapy (IMRT). This applicationdemonstrates the effectiveness of fixed-function theory in S-metric spacesfor modeling and solving practical optimization problems. The proposedresults contribute to both the theoretical development and applied aspectsof fixed-function theory.