  In the present paper, the concept of contraction has been extended in a
refined manner by introducing $\mathfrak{D}$-Contraction defined on a family
$\mathfrak{F}$ of bounded functions. Also, a new notion of fixed function has
been introduced for a metric space. Some fixed function theorems along with
illustrative examples have also been given to verify the effectiveness of our
results. In addition, an application to medical science has also been
presented. This application is based on best approximation of treatment plan
for tumor patients getting intensity modulated radiation therapy(IMRT). In this
technique, a proper DDC matrix truncation has been used that significantly
improves accuracy of results. In 2013, Z. Tian \textit{et al.} presented a
fluence map optimization(FMO) model for dose calculation by splitting the DDC
matrix into two components on the basis of a threshold intensity value.
Following this concept, a sequence of functions can be constructed through the
presented results which contains different dose distributions corresponding to
different patients and finally it converges to a fixed function. The fixed
function obtained in this application represents the suitable doses of a number
of tumor patients at the same time. A nice explanation has also been given to
check the authenticity of the application and the results.
