Some fixed-function results on S-metric spaces with an application to the treatment plan for tumour patients

Abstract

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 setting and ensure the existence and uniqueness of fixed functions in generalized metric spaces. Moreover, the Banach-type fixed function theorem is applied to obtain the best approximation of treatment plans for tumour patients undergoing intensity modulated radiation therapy (IMRT). This application demonstrates the effectiveness of fixed-function theory in S-metric spaces for modeling and solving practical optimization problems. The proposed results contribute to both the theoretical development and applied aspects of fixed-function theory