  In this work we consider a general function for the $c^{2}$ term that appears
in the conventional expression for the holographic dark energy in a FLRW curved
spacetime. The cut-off prospective is inspired in the apparent horizon length.
By exploring the slowly varying condition for the $c^{2}$ term, we obtain a
range of validity for this holographic proposal. Under these considerations can
be found that this holographic cut-off is adequate to describe the late cosmic
evolution. Additionally, by considering some values constrained with the use of
observational data for some cosmological parameters in the context of dark
energy models, such as the deceleration parameter or the parameter state, can
be shown that this holographic model remains {\it close} to the $\Lambda$CDM
model.

General Relativity and Quantum Cosmology;High Energy Physics - Theory