  The original Choi-Davis-Jensen's inequality, with its wide-ranging
applications in diverse scientific and engineering fields, has motivated
researchers to explore generalizations. In this study, we extend
Davis-Choi-Jensen's inequality by considering a nonlinear map instead of a
normalized linear map and generalize operator convex function to any continuous
function defined in a compact region. The Stone-Weierstrass theorem and
Kantorovich function are instrumental in formulating and proving generalized
Choi-Davis-Jensen's inequalities. Additionally, we present an application of
this generalized inequality in the context of statistical physics.
