  One of the greatest difficulties in astrophysics is the determination of the
fundamental stellar parameters (FSPs), one of which is the initial mass
fraction of helium (Y). However, given that Y can be measured spectroscopically
in only a small percentage of stars, a linear relationship is assumed between Y
and the mass fraction of metals (Z). This Y-Z relation is generally represented
as Y=Yp+DY/DZxZ, with the value of the helium-to-metal enrichment ratio (DY/DZ)
assumed as a constant. However, there is no fundamental reason for every star
to have a Y value on a linear scale with Z. In this paper a method for
determining the FSPs of nearby stars is presented that uses at the same time
Mbol, Teff, and log g. One of these parameters is Y, which is used to determine
the validity of the Y-Z relation. A new set of evolutionary tracks is created
using the PGPUC stellar evolution code, which includes 7 masses
(0.5<M/Msun<1.1), 7 helium abundances (0.230<Y<0.370), and 12 metallicities
(1.6x10^-4<Z<6.0x10^-2) for solar-scaled chemical compositions
([alpha/Fe]=0.0). The suggested method is tested using two different
spectroscopic databases of nearby main sequence stars with precise parallaxes,
and spectroscopic measurements of [Fe/H], Teff and g. The proposed method is
compared to other techniques used to determine the FSPs, where one assumes an
age of 5 Gyr for all nearby stars. This comparison demonstrates that the
hypothesis regarding constant age leads to an underestimation of the Y value,
especially for low metallicities. In addition, the suggested method is limited
to masses above 0.60 Msun and requires high-precision measurements of
spectroscopic surface gravities in order to obtain reliable results. Finally,
estimating masses and ages assuming a Y-Z relation rather than a free Y value
may induce average errors of approximately 0.02 Msun and 2 Gyr, respectively.
