  A general class of transcendental equations in complex domain is considered
for functions belonging to the Stieltjes cone. Under certain conditions each
transcendental equation has no solution or one, at most, in the complex plane
cut along the negative real axis. The unique solution is real valued and
positive with an analytical bound. Particular cases consist in transcendental
equations containing exponential, hyperbolic, power law, logarithmic and
special functions. The present approach provides a simple way to prove that
some special functions have no zero in certain sectors of the complex plane cut
along the negative real axis.
